"double post"
Points for creativity, though.
As for the issue of low self-esteem and being competitive, I think some people, including the OP, aren't differentiating between being competitive in a healthy way and being extremely competitive in an unhealthy way. In addition, there are so many permutations for degree of competitiveness and level of self-esteem, and I think you can find examples and explanations for all of them. Perhaps among people with extremely low self-esteem, there might be a guy who's not competitive at all because he thinks he can't compete, but another guy may be highly competitive in an attempt compensate for his own perceived deficiencies. By the same token, for people with extremely high self-esteem, on might not be competitive because he's so secure in himself, while another is overly competitive because he wants to show himself off. The possibilities are endless. This doesn't necessarily mean that self-esteem and competitivenes aren't related, but I don't think they're related in any consistent, predictable way.
Also, I have to agree totally with GoLAClippers about the women and self-esteem issues comment. For most, it's insecurity about their bodies. If it's not their bodies, then it's how they're perceived by other people in terms of personality/intelligence/skill. I have never met a woman who was completely secure in every aspect of her life, but I have met a couple guys who are. They're rare, but they do exist (and, for the most part, are as annoying as hell). But hey, maybe it's just me and the people I've met.