We're Programmed This Way!
If you read up on evolution, one of the key themes is that females are in competition with one another. Our female brains are programmed to desire the strongest, healthiest man who will father healthy babies to keep the human population existing.
Since we're supposed to be competing, it's pretty hard to form a true friendship. We could, however, form a bond if it helps us reach our goal of finding a hot mate. In my opinion, that's why the prettiest girls in school will form "packs" and hang out together. If there's a whole tribe of good-looking girls, the strong, athletic jocks are more likely to notice them. The prettier girls will also exclude the less attractive girls, as they may repel their potential mates. It's also inevitable that the pretty girls will backstab each other, and it will almost always involve fighting over guys.
We might just be animals doing what are brains have been programmed to do for centuries.
The good news is, it becomes easier for females to become friends later in life, when we already have mates and don't care to compete for any more.