Because people base their morals off of their spiritual beliefs, for the most part.
I mean, even I do, and I'm not particularly religious.
But you're right, the problem is when people use that justification to apply to other people as well, and not just guide their own beliefs.
Perhaps it's because christianity is the only religion that seems to think it's the only religion. (I hope that made sense) Therefore, christians seem to think they have a responsibility to witness the truth to others.
I'm not trying to say that in a bad way, I have experienced being a christian and most of them are really just trying to do what they think is right and best. Christians witness (or should) because they care about your soul. Probably more than you all do!! Lol.... (myself included)