I'm not exactly competitive, but it's my instinct to peddle as fast as I can. Mind you, that's not all that fast, but I do tend to go faster than a lot of folks tooling along the bike paths. I find it really annoying if I come up behind someone. There often isn't room to pass, or I'm not going enough faster that passing makes sense. And if I do pass, all too often a block later I hit a light, the other person catches up, and we play the same game all over again.
I think I just needto learn to slow down and mellow out a little. Given lights, traffic, wayward pedestrians, etc. etc., pedaling faster doesn't get me to where I'm going faster, it just gives me more time to wait at the next light. I think I just hate the feeling of being penned in, and having to go someone else's pace, even if going my pace doesn't really gain me anything. On long open stretches, which pretty much means the greenway along the river or the bridges, I pass and get passed all the time with no issues.