I'm wondering WHY a strong belief in rebirth does not conform with the above Buddha's teachings?

Because in the western history, the western people have suffering by some religious, that have a strong belief in rebirth through moreover 2000 years, so they hate that religious and that belief, together. when they catch the buddha's teaching, they bias the buddha's teaching by that hate. They try to cutting rebirth off tipitaka, although they never completely study throughout the buddha's teaching by an ancient study system