Achilles was willing to sacrifice his life for the sake of his pride because he did not listen to the advice of others and protect his achilles heel, the only place where someone could kill him. Achilles couldn't be killed except if you were to shoot an arrow into his heel, so by not protecting his heel, Achilles pride got in the way which lead to his death. He ended up getting shot by a poisoned arrow in his heel and died. Achilles was willing to sacrifice his life for the sake of pride. He sacrificed something huge for something so small.
