There are several concepts that are the core of Christianity. The Cross, free-will and judgement (punishment and reward) top the list. These basic concept of Christianity contain contradictions in them.
The Cross demands free-will but at the same time negates it. It says choose Christ for he is good, and you couldn’t choose good so you need Christ.
As far as judgement, heaven and hell, there is a serious problem. We were deceived but responsible for our sins and culpable for eternal judgement. We have intentionally chosen the bad, but could not help it. We have chosen a short, insignificant life instead of choosing an eternity of pleasure—if we did not choose to be a Christian. But we cannot choose to be Christian because he is the “author and the finisher of our Faith”, and “Faith is a gift from God” and “he knew [us] before we were formed”—and we have an sinful nature which naturally choses bad.
In addition there is Aristotle’s paradox: people always choose what they see as good. If we always chose what we see as good, then we will choose the best good we know. If we only know this pleasure or that pleasure we will always choose this or that pleasure–unless we know something better. If we know something better, we will choose that. If heaven and the things we do for it are the good and lead to the highest pleasure, then if we really knew or were naturally constituted to see heaven, and the like, as best, then we would choose that. Unless, of course, we don’t know what is best, then we would chooses something else or, at best, choose the good on accident. So, in some sense, to always strive for the good, means we are good by intent: it is always the outcome that is wrong. So we would be judged for our crimes, crimes that simply were just a mistake of action (not of intent) and not a crime of morality—since we always choose what we think is good. You might say that we might want to choose the bad, the genuinely evil, but then we would have to be choosing it for something that makes it choice-worthy; and, so we would be choosing it for the perceived goodness that makes it choice-worthy, so we are always intent on the good.
So Christian doctrine, at its core, holds that free-will and not freewill, that people are liable and that people are not liable.