Why did people pick up rocks to throw at Jesus after He said Before Abraham was I am?

Answer 1

Because by saying that, in the mind of the Jews, He was saying He was God because He had always existed, and many of the Jews refused to believe He was God, and they considered it blasphemy for any man to say he was God.

Answer 2

People picked up rocks to throw at Jesus because they considered His statement to be blasphemous. By saying "Before Abraham was, I am," Jesus was claiming to be God, which was seen as a violation of Jewish law and a direct challenge to the religious authorities of the time. So, the people reacted with anger and sought to punish Him for what they deemed as blasphemy.