Why do you think Amir recalls this memory when he witnesses Hassan's tragedy in the alleyway?
A strong thematic parallel is suggested here between Hassan and the sheep whose sacrifice Amir had witnessed. Both Hassan and the animal are innocent of offense; both are powerless, victimized by forces beyond their control.
The reference to the sheep’s eyes implies that Amir saw something in those eyes that continues to haunt him: fear, confusion, and suffering—emotions Hassan experiences during the brutal attack he endures.
Finally, the concept of animal sacrifice completes the thematic parallel. As a religious rite, an animal was offered up to a greater power for the well-being of those making the sacrifice. By choosing to take no action to save his friend, Amir effectively offers up Hassan to the bullies attacking him in order to secure Amir’s own safety. Hassan is sacrificed on the altar of Amir’s fear and cowardice.
At the moment of Hassan’s greatest agony, Amir recalls the sacrifice of the sheep: Consciously or subconsciously, at that moment he recognizes the truth about himself.
It has alot to do with the eyes. Hassan's eyes in the novel are often described as 'open' and guileless. A sheep's eyes during that final moment of sacrifice are the same. The sheep seemingly resign themselves to their fate and quite often do not struggle even as their throats are slit.
Hassan's sacrifice in the alleyway could be seen as Hassan becoming the 'sacrificial lamb' not because he wants to be but because he has been outnumbered by Assef and his two friends and is resigned to his fate, knowing that Amir (or anyone else for that matter) will not come to his rescue. His initial fight could be perceived as a matter of hope as well- he fights back in the hopes that someone would save him from his assailants.