If I'm literally competing to earn a living, or if it ends up in praising winners and blaming losers, it won't be enjoyable, and I'd rather not play at all. Having humility also means that when you win, you also congratulate losers for playing.
I agree that we need to compete on some aspects, like technology, science, construction methods, and business in general. But competing between individuals brings out the worst in people. And that's where exclusion starts: if you keep slapping people's self esteem by telling them that life and society is a game of winners and losers, you'll end up with less and less people ready to take part in it.
Overall, I sense that men avoid competition much more than women do. Or maybe it's the political climate that does. I don't really know.