To illustrate the difference between positive and negative competition, I'm going to give you an allegorical narrative of a table top with a book on top of it. We will call this Book A. However, you have another book in your possession that you wish to put on the table top as well. We will call this Book B. To do this, however, you have only three options:
1. You can swat Book A off the table and put Book B where Book A was.
2. You can place Book B on top of Book A, completely overshadowing Book A.
3. You can place Book B next to Book A.
Now, any rational personal realizes that option 1 is silly, leaving them with only two possibilities. But lets pretend for a moment that our books have emotions and egos. Now what do you do?
You can put one book over another, thereby sating the ego of one, but crippling the other. As well, option 2 starts to become less appealing and we are left with option 3, where we both books are visible to anyone crossing the path of the table top and have equal opportunity to be noticed.
If you see where I'm going with this, pat yourself on the back. If not, that's okay. Essentially, Book B is you. And Book A is those you interact with.
The point of my narrative was to illustrate the point that you do not need to knock off one thing to showcase another. The same works in everyday life, wherein you can aggrandize yourself without diminishing the worth of those around you. Realistically, in doing so, you do not grow by doing this; all you do is feel superior because those around you are growing smaller rather than you growing larger.
Now, understand that it is good to be competitive. Always strive to be the best in all of your dealings, but don't be immature about it. This is the difference between positive and negative competition.
A positive competitor will work on his sports team as a cohesive unit. They will look to be the best on their team, but still look out for those around them. And every time they get better, they will work to make those on their team come to their level as well. Then, when everyone is equal again, they will look to be the best once again. This is a healthy form of competition, where everyone benefits from working hard.
A negative competitor, however, is what many of us would call a "ball hog" or a "glory hound". They're not interested in the team being victorious; they just want to be noticed. They belittle those around them and actively look to sabotage the progress of their team mates. This is not a healthy form of competition and worse, it makes everyone on the team worse, including yourself. Not to mention you'll be awfully lonely.
Naturally, you wanna be the former and not the latter.