I agree with Mark L and think many fighters get so obsessed about being number one that it makes them a lot more rigid in their style. When you're mind is focused purely on winning you're more likely to want to punch/kick the finishing blow in each exchange instead of calmly rolling with the punches and naturally seizing the right opportunity as it comes. When both fighters get rigid with the idea of winning it's just like watching cat fight.

Yet at the same time the opposite extreme is also something to be cautious of. I was sparring a few nights ago with a girl at my dojo who is my senpai (senior) and because of her seniority alone she believes she's better.. in Japan the excess in ego comes out in strange and mysterious ways... so she stands still as I punch and kick, and in her mind she believes she is strong and superior and that my blows don't mean anything, but she quickly lost control of herself in her attempt at being martially holier than thou and was unable to regain a strong stance.

So perhaps it's a balance of attempting to win yet not be afraid to lose, while releasing our true form mentally and in our martial technique that's most natural to us.