Why was Eliezer glad that he had forgotten seeing Rabbi Eliahou's son?

During the forced march from Buna to Birkenau, Elie sees Rabbi Eliahou while the Jews seek shelter from the snow in an old brick factory with a collapsed roof. The rabbi was separated from his son during the chaos of the march and he is now looking for him. He asks Elie if he has seen the boy, but Elie indicates he has not. Just after the rabbi has left the shelter Elie remembers that he had seen the rabbi's son attempting to distance himself from his father. Elie says,

A terrible thought loomed up in my mind: he had wanted to get rid of his father! He had felt that his father was growing weak, he had believed that the end was near and had sought separation in order to get rid of the burden, to free himself from an encumbrance which could lessen his own chances of survival.

Elie further notes that he "had done well to forget that" and happy the rabbi "should continue to look for his beloved son." Elie would rather see the rabbi continue searching than to admit that the son was content to see his father die. The episode seems to mirror Elie's own situation with his father who has also grown quite weak and is also a burden. In contrast to the rabbi's son, however, Elie never abandons his father and stays with him until his death at Birkenau. In fact, the thought of leaving his father may have saved Elie's life during the march when he almost succumbed to the pain in his foot and stopped, which would have meant certain death. He says,

My father's presence was the only thing that stopped me. . . . He was running at my side, out of breath, at the end of his strength, at his wit's end. I had no right to let myself die. What would he do without me? I was his only support.