Why did Buddha praise the vedic Agnihotra as the foremost sacrifice?

Why Buddha praises the vedic Agnihotra as the foremost sacrifice and the Gayatri mantra as the foremost meter in the Pali Canon?

aggihuttamukhā yaññā sāvittī chandaso mukham.
Sacrifices have the agnihotra as foremost; of meter the foremost is the Sāvitrī

"On the Buddha's Use of Some Brahmanical Motifs in Pali Texts"

Above quoted text is from M.N. Sela-Sutta, that buddha taught to selabrahmaṇa:

aggihuttamukhā yaññā sāvittī chandaso mukham.
Sacrifices have the agnihotra as foremost; of meter the foremost is the Sāvitrī

So, buddha didn't taught veda. Buddha just use selabrahmaṇa's knowledge, veda, to teach him the last line:

puññaṃ ākaṅkhamānānaṃ, saṅgho ve yajataṃ mukha’’nti
Saṅgha is the best foremost of wholesome-mind developers.

This last line is the real buddha's teaching. Your quoted line, veda, was used by buddha just as alike as a tool to make selabrahmmaṇa understand the last line.

How can you taught new language for a foreigners? You use their knew-language to teach them new language, right? That is what buddha did.

Doubts in Buddhist Teachings Abandonment Method

Abhidhamma is the answer for doubting person (vicikicchā-mind-factor just arise with pure moha-mind).

Commentary said that in 3 pitaka:

1. Vinaya-pitaka is for alobha-meditation.
2. Sutta-pitaka is for adosa-meditation.
3. Abhidhamma-pitaka is for amoha-meditation.

Why?

One must leaves every lay's asset, lobha's object, for observing vinaya in vinaya-pitaka. So, vinaya-pitaka is for alobha-development (ordinate to observe monk's sīla).

One must leaves every kāma-loka's senses by jhāna, for living like bhrahmma-deva, like anāgami done. Kāma-loka's senses are causes of dosa, too. Therefore anagāmi, who abadoned paṭiga-anusaya (dosa), abandoned next life in kāma-loka, too. And sutta is very less description, very short, and very less question, when compare with abhidhamma, because buddha taught sutta for the listeners who had experiences in upacāra-jhāna, appanā-jhāna, or upacāra-jhāna-like (ditthi-caritta [uggaṭitaññu & vipacitaññu]). Samahitam cittam yathabhutam pajanati (Good concentrating practitioner will see the truth). So, suttanta-pitaka is for adosa-development (concentration-meditation).

Buddha taught abhidhamma to sāriputta very long description and sāriputta taught paṭisambhidāmagga & niddesa very long description, too. Also, there are millions questions in those canons. Because buddha and sāriputta taught abhidhamma-pitaka for the listeners who have a ton of questions, low concentrating in meditation object, and too much doubts. So, abhidhamma-pitaka is for amoha-development (wisdom/understand-meditation).

So, if you want the answers for every doubts, full-course abhidhamma-study is required by your doubt. Everything in abhidhamma must can analysis their own reasons (causes and effects). So, your doubts can not doubt anymore, after you understand throughout abhidhamma.

Why talaputta sutta wrote actors will go to hell?

In Talaputta Sutta:

When an actor on the stage, [he thinks that] after death, he is reborn in the company of the laughing devas,' that is his wrong view. Now, there are two destinations for a person with wrong view, I tell you: either hell or the animal womb.

An actor is a mijjhā-ājīva in 8-mijjhā-magga, akusala-kammapatha-offense career that buddha said "reborn in hell", because it is 7th of 10 akusala kammapatha, that is micchā-jāca, samphappalāla-akusalakammapatha. And that mijjhā-ājīva is wrong livelihood in vanijjasutta (english translation).

The actor/singer career is direct hindrance career for the meditations, because 8 fold path require right speech and right action of right career first as adhi-sīla (observe-practice that is an important base of meditation-practice, higher level practice).

Should Lay Buddhists Teach the Dhamma?

Yes, if he as enough knowledge.

The required lowest graduation:

Qualities of enlightened lay teacher for lay people:

1. Enlightened sodāpatti-phala, at least.
2. Proficient to recite and to understand 9 pāṭha, the whole K.N. khuddaka-pātha, and their commentaries.
3. Proficient to recite and to understand the whole K.N. Itivuttaka, and their commentaries.
4. Enough understand to judge/to decide about 8 precepts.
5. Enough understand to judge/to decide about abhidhamma in his kammaṭṭhāna. This abhidhamma knowledge will come with his meditation and his enlightenment, no need to study. However, more abhidhamma knowledge is required for teaching the other qualities below, so lay teacher must study this part, such as Cittagahapati did.
6. 5 years experience in buddhism.

I sum above qualities myself from the profile of lay-etadagga, such as Khujjuttarā, Cittagahapati.
However, the pāli canon never focus on lay teacher, because the ariya-lays very respect bhikkhu. So, they often invite bhikkhu to teach, first. But khujjuttarā can not invite bhikkhu into the king's palace, so she must recite & recollect tipitaka herself to teach inside the king's palace.
Another, if lay teacher will teach bhikkhu, he need this Qualities, that was writen in commentary according to V.N. Mahākhandhaka:

Qualities of nissayamuccaka-bhikkhu (teaching lay people)

1. Proficient to recite pāṭimokkha-pāli and to understand it's commentary.
2. Proficient to recite and to understand 4 bhāṇavāra (~1,000 syllable) of sutta and their commentary, to teach laymen on uposatha day.
3. Proficient to recite and to understand sutta for bhikkhu's life such as andhakavindasutta, mahālahulovādasutta, ambaṭṭhasutta, etc.
4. Proficient to recite and to understand sutta for teaching in 3 chances: banquet for saṅgha by layman (nidhikaṇdasutta), funeral ceremony (tirokuṭṭasutta), and auspicious ceremony (maṅgalasutta).
5. Enough understand to judge/to decide about saṇgha's ceremony such as uposatha, pavāraṇā, etc.
6. Proficient to recite and to understand his kammaṭṭhānā throughout the nibbāna-course.
7. 5 years experience in monk hood as a monk.

Qualities of bhikkuparisūpaṭṭhāpaka-bhikkhu (teaching bikkhus)
If above layman's teachers want to teach bhikkhus (ūpajjhā-ācāriya, nissaya-ācāriya), they must increase their skill level to all of the following qualities.
These are for abhivinaya teaching:

1. Proficient to recite mahāvibhagha and bhikkhunivibhaṅga (first 3 books of thai 45 books pali-tipitaka) of vinaya-pitaka-pali. At least, he can relay with the other 3 bhikkhu. Proficient to understand it's commentary, too.
2. Proficient to recite all saṇgha's ceremony in vinaya-pitaka mahāvagga and julavagga.
3. Proficient to recite 14 vatta in vattakhandhaka.

These are for abhidhamma (kammaṭṭhāna) teaching:

4. Proficient to recite one of this suttanta-pali: mūlapaṇṇassa (1st/3 parts of M.N.) for student in M.N. faculty, mahāvagga (2nd/3 parts of D.N.) for student in D.N. faculty, sagāthavagga+nidānavagga+khandhavāravagga of S.N. or mahāvagga of S.N. for student in S.N. faculty, before half of A.N. or after half of A.N. or ekakanipāta+dukanipāta of A.N. for student in A.N. faculty, jātaka+commentary (because kammaṭṭhāna was described in commentary) for student in jātaka faculty.

Qualities of bhikkunovdaka-bhikkhu (teaching bhikkunīs)
If above layman's teachers want to teach bhikkhunī, they must increase their skill level to all of these qualities:

1. Proficient to recite whole tipitaka-pali and commentary-pali. Or at least, he still must recite whole tipitaka, but he can recite just one commentary of suttanta, first 4 parts of commentary of 7 parts of abhidhamma. However, vinaya-commentary is what he must recite it all.

Reference: tipitaka and commentary of vinaya pācittiyakaṇḍa bhikkhunovādakasikkhāpada and vinaya mahāvagga mahākhandhaka.

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Related topic: https://buddhism.stackexchange.com/a/22917/10100

Buddhism is intellectualism or not?

https://buddhism.stackexchange.com/a/23643/10100

Buddhism is middle way between intellectual self-affliction extreme and intellectual sensual pleasure extreme.
So, buddhism is anti-intellectual self-affliction extreme and anti-intellectual sensual pleasure extreme. But buddhism is the middle way intellectualism.

The object is not to gain anything. Intellectual knowledge can help but little intellect is required. Sometimes it can get in the way.

I can completely say according to tipitaka history that most of ariya in tipitaka are intellect, high experience, high profile, and intelligence, before they enlighten to be ariya. And for someone who has a very low profile, he has to take a very log time to practice himself for enlightenment.
If you learn commentary and abhidhamma, you maybe say "how many millions of required life for tipitaka study and practicing?"
But deplorably, the most people can take just an easy part of tipitaka, so you can feel like you asked above.
However, whatever you stared from, little intellect or big intellect, must develop to be big intellect for enlightenment, no exception. That is the reason that why the buddhist have to practice. We practice to be intellect enough for an enlightenment.

Western psychology's willpower and buddhism

Tipitaka is teaching about the best willpower for recieving the 6 profit: this life profit, next life, nibbāna profit, own profit, the others profit, and social public profit (atthattha, parattha, attāparattha, diṭṭhadhammattha, samparāyikattha, and paramattha).

Target of every teaching in tipitaka is just nibbāna profit, if not, it is not buddha's teaching. It is just the other religious teaching, although that religious member can attains wholesome jhāna (añña-titthiya/diṭṭhi in V.N. Mahavagga Mahākhandhaka).

But the path to enlighten nibbāna profit, is an eightfold path, path with eight element, so the practitioner who ้heading to nibbāna must manage and dedelop/meditate eightfold path's elements.

These eightfold path's elements is the cause of nibbāna profit and the other 5 profits, too. Also, buddha taught to meditate eightfold path. So, tipitaka is teaching about the best willpower.

For more explanation:

You avoid your gift for monk by giving monk gift, to receive the higher gain from that monk such as adhi-sikkhā teaching, higher class study, more than just drunk in that gift, lower class.

You avoid your hell view physical happiness by observe the adhi-sīla, to receive the meditation-chance.

You avoid whole your present physical happiness by meditate concentration meditation, to receive the insight-meditation-chance.

You avoid whole your future happiness by meditate insight-meditation, to enlighten nibbāna.

The received chance is fruit that come with the other 5 profits, too.

So, tipitaka is teaching about the best willpower.

What makes someone an “insider” or an “outsider” according to Buddha Dharma and Sangha

Tipitaka is teaching about "How to receive the whole 6 profits": this life profit, next life, nibbāna profit, own profit, the others profit, and social public profit (atthattha, parattha, attāparattha, diṭṭhadhammattha, samparāyikattha, and paramattha).
Target of every teaching in tipitaka is just nibbāna profit, if not, it is not buddha's teaching, outsider. It is just the other religious teaching, although that religious member can attains wholesome jhāna (añña-titthiya/diṭṭhi in V.N. Mahavagga Mahākhandhaka).
There may have many teaching that available in the other religious, too. However, just buddha can be the first teacher who can teach that how to get the whole 6 profits, because only buddha can enlighten anatta by himself and teach to the other.

9. "Bhikkhus, there are these four kinds of clinging. What four? Clinging to sensual pleasures, clinging to views, clinging to rules and observances, and clinging to a doctrine of self.
10. "Though certain recluses and brahmans claim to propound the full understanding of all kinds of clinging, they do not completely describe the full understanding of all kinds of clinging.[7] They describe the full understanding of clinging to sensual pleasures without describing the full understanding of clinging to views, clinging to rules and observances, and clinging to a doctrine of self. Why is that? Those good recluses and brahmans do not understand these three instances of clinging as they actually are. Therefore, though they claim to propound the full understanding of all kinds of clinging, they describe only the full understanding of clinging to sensual pleasures without describing the full understanding of clinging to views, clinging to rules and observances, and clinging to a doctrine of self.
11. "Though certain recluses and brahmans claim to propound the full understanding of all kinds of clinging... they describe the full understanding of clinging to sensual pleasures and clinging to views without describing the full understanding of clinging to rules and observances and clinging to a doctrine of self. Why is that? They do not understand two instances... therefore they describe only the full understanding of clinging to sensual pleasures and clinging to views without describing the full understanding of clinging to rules and observances and clinging to a doctrine of self.
12. "Though certain recluses and brahmans claim to propound the full understanding of all kinds of clinging... they describe the full understanding of clinging to sensual pleasures, clinging to views, and clinging to rules and observances without describing the full understanding of clinging to a doctrine of self. They do not understand one instance... therefore they describe only the full understanding of clinging to sensual pleasures, clinging to views, and clinging to rules and observances without describing the full understanding of clinging to a doctrine of self.[8]
13. "Bhikkhus, in such a Dhamma and Discipline as that it is plain that confidence in the Teacher is not rightly directed, that confidence in the Dhamma is not rightly directed, that fulfillment of the precepts is not rightly directed, and that the affection among companions in the Dhamma is not rightly directed. Why is that? Because that is how it is when the Dhamma and Discipline is [67] badly proclaimed and badly expounded, unemancipating, unconducive to peace, expounded by one who is not fully enlightened.
14. "Bhikkhus, when a Tathagata, accomplished and fully enlightened, claims to propound the full understanding of all kinds of clinging, he completely describes the full understanding of all kinds of clinging: he describes the full understanding of clinging to sensual pleasures, clinging to views, clinging to rules and observances, and clinging to a doctrine of self.[9]