You should read some about Moral Skepticism, as I am doing now. It's really fascinating, but I'm not claiming to be an expert. It's hitting home with a lot of my beliefs, though.
Let's take the instance you said, someone steals my car (this is a good one because I just bought a car and I'd be really upset if someone took it). From my point of view, what they did is wrong. I find it wrong to steal, whether it be my car or someone else's. That's why I don't steal.
However, from their point of view, maybe it wasn't wrong. Maybe in their eyes, they really deserved the car. Does that justify what happened? No, I don't think so. That's why I think there should be legal repercussions for people who steal. However, from a moral point of view he didn't do anything wrong, because my opinion that it was wrong isn't universal. Despite the fact that the vast majority of people think that stealing is wrong, that doesn't make it true, because all it is is an opinion.
So your last question, "if they are only wrong for you, why are they not right for someone else?" That's just it, it is right for someone else!