Why will God punish people for the sins that Jesus Christs already was punished for?

Because they do not accept him. A person has to accept God, Jesus, and their forgiveness before they can be forgiven. Would you like to live your life with people doing wrong to you and never apologizing? They would just go on like it was nothing, and expect you to act like it never happened. I sure wouldn't want to live that way, and neither does God.