Shouldn’t we be accountable for our own sin and not rely on another to pay our penalty?

Why does Christianity teach that Christ has paid the penalty for our sins? Isn’t this unfair since one should be accountable for his actions and not rely solely on another person to save him.

There was a story about a young woman who was caught for speeding. She was brought to court where the judge pronounced a fine of $100. After that, the judge did a surprising thing. He got down from his chair and walked down to pay the fine. You see, the judge was the girl’s father. But being a judge, he has to be just and pronounce the sentence. But because he loves his daughter, he is willing to take the punishment himself.

No one listening to this story would think that it is unfair for a father to pay for his daughter’s fine. The fine has to be paid and it is perfectly normal for a loving parent to want to help out his child if it is within his capacity.