There is a simple explanation to this phenomenon:

(A)There are not enough good looking + nice + everything a girl wants kinda guy to go around and therefore "I must be prettier than her" notion comes about.

(B) Some girls are very self-absorbed when they tend to get a lot of compliments and therefore they'd like to APPEAR to be better than the other girls. To do so, they must sabotage your positive opinion on the other girls. In other words: some girls think they're better therefore you must think so too.

(C) In contrast with (B), some girls have such low self-esteem that they try to make themselves feel better by putting other girls down.

There are obviously many more reasons to girl-girl competition but I just can't think of anymore right now.