We can't see nibbāna, because of diṭṭhi-clinging. Nibbāna is the opposite of the dependent origination.

The dependent origination are the cycle of happening/cessation conditions.

What is the dependent origination?

It is every true things, except nibbāna.

What is nibbāna?

It is the truth which is the opposite side of the dependent origination, the opposite side of the cycle of happening/cessation conditions. Nibbāna never has happening/cessation conditions. The conditions can know nibbāna, but they can't let nibbāna arise or vanish.

Why we can't see nibbāna by thinking like the noble ones can do?

Because we still having the wrong understood about the dependent origination, diṭṭhi-clinging, so we can't daily understand&discover&make cessation of the truth's root conditions, avijjā&taṇhā&all-unwholesome. Therefore we can't see nibbāna like the noble ones can do.

How to see nibbāna? 

Observe sīla, meditate samādhi and vipassanā until enlightened.

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The popular question about nibbāna already answered in Ekādasamo paricchedo Nibbānaniddeso of abhidhammāvatāra.

There also are many aspects of nibbāna in Abhi. Kathāvatthu as well.