Anders, I understand what you're saying. I don't believe in the Bible, but if I did, I would argue as follows:
There's a difference between my forgiving you and Jehovah forgiving you. They're the same word but they don't mean the same thing. When I forgive you, first of all, it implies that you made a mistake against me. And second of all, it implies that I don't bear a grudge against you because of what you did against me. When God forgives you, it has a whole different meaning. First, he holds you accountable to standards of righteousness - it's not just about you hurting him. Second, his "forgiving you" means viewing you as a righteous person, recognizing your status as blameless.
The difference between these two is illustrated by what happened when Jesus "forgave" people's sins, the Pharisees went all crazy, "what authority does he have to forgive sins?!" Obviously they knew that anyone could forgive anyone for offenses committed against them. But Jesus was forgiving in the larger sense, and that was tantamount to blasphemy in their eyes.
When we keep in mind this second, larger sense, we can better understand why the Bible mentions the needs for a ransom. Again, I'm not saying I believe it :)