Alex : "Demonstrably false. As a parent, I am not obligated in any way by my child's behavior; I choose, however, to match my rewards and punishments to what the child actually does, because I love my child. There is no mystery in this."
Your comparison doesn't work because you are a flawed human (no offense :) and are capable of being inconsistent (partial), or even not keeping your word. Does God do that? The Bible gives us specific promises as to how salvation works. We believe it is by grace through faith, and you say it is by works and the Church. If God is impartial, then there must be some minimum number of works (or type) that are necessary to OBLIGATE God to save us, along with the Church. If you say "no", then that only leaves God being partial, AND/OR God not keeping His word.
But my flaws are not of essence for the comparison. Even if I were wholly consistent, all-knowing and impartial, I still would not be obligated to give my child what I do not wish to give. I may offer a deal: get on the honor roll and you can have a dog, — but that is still my decision to offer the deal. Nor is it wrong for the parent to offer these deals on an indivudual basis, taking into account the condition of the heart of each child.
Likewise, while God judges us by our works, he does not judge us by any human measure of the work. This is very clear from the parable of the workers in the vineyard. Divine justice is mercy; we cannot comprehend it. In fact, one who does the work of charity thinking that he obligates God, rather than in the spirit of humility, is guilty of presumption, together with the self-righteous pharisees.