Well Bladesinger maybe the problem you are having isn`t something so simple a problem as you think. Despite what many would like to believe christianity is not a religion. And there is no complete parralel to christianity. There are many religions, which happen to have astonishing similarities to it but they don`t take it to the fullness that God intended for it to go. What christianity really is, is a relationship between you and Jesus.
As for the more simple question of Christ dieing for our sins. That is a fact the real question should be do you think Christ was a lunatic or not.