"Morality" covers a large range of actions, from being simply being polite all the way to obeying laws and norms when one doesn't feel like it. I was taught by my parents how to behave in our society in order to be accepted, and apparently it took. They were taught by their parents, and they by theirs, ad semi-infinitum.
For whatever reason, I agree with the polite stuff, and I don't mind helping little old ladies across the street. I would feel the same way if I were the most pious christian on the planet. At least I hope I would. I have no disagreement with civilized behavior.
Like the rest of us, I like living in a world where I don't have to worry about every human I see. Enough of us are civil enough that things generally work.
My non-christian stance has little to do with my overall moral expectations of myself. Having decided I don't want to get bopped over the head on a regular basis, I, without religious guidance, decided to not bop other people over the head in hopes that it would stave off such behavior in others. And with rare exception, it's worked fine. I have no quarrel with the more practical commandments such as the one that mentions in a half-hearted way that we shouldn't kill. I say half-hearted because way too many christians consider that a suggestion rather than a commandment. It didn't seem to bother George Bush II when he attacked Iraq under false pretenses. If I'm going to do something that is wrong, I'm not going to lie to myself about it. Nor anyone else.
I don't need a belief system to participate in civilized behavior. I need only agree in principal and fact with enough of the social rules to be considered normal. I'm not perfect, nor is anyone else. But I don't do any of the big bad things (kill, steal, embezzle, run a bank) and that seems to be good enough for most people. As it is for me.
There are all sorts of psychological and social studies that try to study or define morality, and I'm sure this discussion will play around with a few proposed reasons, but that is making it way too complicated. Morality defined by a committee of researchers and scientists is probably just as mucked up as anything else decided by committees, and so i don't pay too much attention to such things.
I'm too busy being a generally nice guy to bother. Even though I'm a full-blown atheist.