I'm not a competitive person. At all. If I talk about myself it's just me trying to relate to other people, to avoid feeling alienated. I don't "one-up" people. I don't think I'm smarter, prettier, funnier, more talented, or in any way better than other people. And in the cases where that might be categorically true, I don't care: they have other skills that are superior to mine, it all balances out, etc. My point? I can't stand being accused of think I am, or trying to be better than another person. I repeat, if I say "I've done that, too" or "I also..." etc, what I'm saying - and what I assume other people mean, when they are saying similar things to me, is "Hey, you're awesome, and have just made me happy by reminding me of a great experience I once had!" or "Hey, that was an awesome idea, I'm inspired!" Not sure how or why this became an issue - perhaps it's the pseudo-celebrity culture that abounds on the internet, or perhaps it's human nature. I don't follow that culture, though, and a long, long, long time ago I learned that competitiveness and snobbery serves no purpose.
If you want to be the best, work hard and accept opportunities as they come. You don't have to cut other people down to get there.