When he was getting raped
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There are so many reasons for this. I think the first one is that he was simply scared. Assef was a bully/sociopath. Interfering would have got Amir hurt. Then there the many socio-cultural implications of coming to the aid of a Hazara.
He was also jealous of the attention Hassan got from his father, Baba, whilst he on the other hand had felt neglected. He felt that in order to "win over Baba" he would have to 'take down' Hassan (??) - "Maybe Hassan was the price I had to pay, the lamb I had to slay, to win Baba". He tries to make himself feel better for his betrayal through viewing Hassan as "only a Hazara" who was therefor, no matter what trauma he endured, an insignificant person especially in the Afghanistan social values.