As it is a very complex question on a multifaceted subject, it should be addressed as such. First of all, if we genuinely seek an answer, let us decide what answer we seek because it influences how evidence is viewed. We straight guys are very much encouraged to believe women exist in relation to us and not as individual human beings. That is why cultures which endorse "second wives" as they're called in Southeast Asia have so frequent mistress fights. If that is what we are to discuss, the reasons are but a few.
I work as a freelance writer, have worked in the hospitality business and in customer support, in other words, fields with female dominance (which is mostly because these are jobs most men don't want to do). That is to say the social hierarchy of women is not different from that of men and an equal bottle necking exist (you might know this better as a glass ceiling) where resources are intentionally distributed unevenly so that internal conflict within organization take the load off of having to make hard and tough decisions.
Ever since cities became a thing followed by organized religions, the public hierarchy was created that "real" positions can be only held by men and lesser functions are to be inhabited by women. The more socially conservative the circle you come from the more you're likely to believe women have no ambitions. In contrast, these strength admiring hierarchies have been established so that self-righteous people don't have to "suffer" such processes like having their ideas challenged. That way they also don't have to fight to keep their position or fight to keep resources they lord over.
As individuals, the reasons for women to fight varies in reason, intensity and temper. It can be spontaneous like a road rage, or planned. It can be a personal conflict, or just as sinclairfan says a conflict borne out one of them gaming the system to their own benefit. It can be a class issue, and spoiler alert, if you don't live in a country with a rich economy, it can be nationalism, or even straight up bigotry, like a racist of sexual based hate crime.
Heck, sinclairfan's Memel story might be fiction (and I encourage all of you to read it), that situation has not changed in a century. So all in all the question depends on the answer you seek, but I do know it for a fact women don't like their serious conflicts be reduced to sexualized catfights.
