I agree that problems with "competitive parenting" tend to occur when the parent is overly invested in the child's accomplishments. Perfectionist parenting doesn't work, but that doesn't keep (us) perfectionists from having kids. (!)
In addition to perfectionism, a big part of the problem, I think, comes of parents who are used to being top achievers suddenly having nothing of their own to do anymore except raising the kids. I was a high-achiever, and being reduced to repeating the alphabet ad nauseum (because it was my son's obsession from ages 12mos-16mos or so) was just killing my soul. I actually taught myself to whistle during that time because I was so bored. It took lots and lots of practice, but it gave me something to do that was my own project. By the time I had my second child, I needed more, and it's one of the reasons I started writing the novel. It was that or go back to work...or lose my ever-lovin' mind.
Don't get me wrong: I love being a stay-at-home parent and I wouldn't trade my time with the kids for anything. But it was never easy for me. If I hadn't realized what a strain it was for me and made sure that I had my own life, too, I think I could have become too invested in my kids' accomplishments and become one of those competitive parents. So I have a lot of sympathy.
My solution: when confronted with someone who wants to be a rival, I refuse to join the fight. I pull out my standard, "Yes! It's so great what your child can do. Amazing! They all develop in their own ways, don't they? It's such fun to watch them grow and learn."
It seems to diffuse the competitive spirit almost immediately, though with diehard competitors, it might take a few repetitions. If the person really won't let it go, I avoid him/her. But I've only had to do this once. It seems that competitive parenting is usually only fun if there's someone to compete against.
