Setting this up was a great idea, this is something we all can enjoy talking about.
I gave it some thought and came up with some theories for this.
Theory #1
The living and the undead all belong to the same universe. They have conflicting natures.
For whatever reason, either the living have a prejudice against the dead, or the dead have a kind of prejudice against the living, or both. Maybe the living have no regard for the undead's space, or they have been weakening the life source of the undead, or they want to use them as slaves, or they have been contributing too much to the rise of undead and their population is overgrowing. Hahahha... In any case, their differences is enough that they can't stand each other. Pure hate motivates their fighting.
Theory #2
The living and the undead all belong to the same universe. The living sought to control and use the undead.
For whatever reason, and in whatever manner, the living found a way to control the undead. Either through necromancy, or the use of artifacts or magick, or both. They have this power and they decided to use it, either to gain more power, or to fight against each other, or simply because they could. The undead might resent being manipulated like this, and have sought a way to free themselves.
Theory #3
The living and the undead belong to different universes. The living brought the undead to their realm.
Perhaps to use them as a weapon, as slaves, as a plague, it doesn't matter. Someone used the world's power, in the form of artifacts, magick and material manipulation, to give birth to the first undead, thinking they could control them. But they couldn't, and the undead eventually gained sentience--or strengthened their sentience--over time and decided that they deserved better than be subjugated by the living... and thus, revolted against them.
Theory #4
The living and the undead belong to different universes. The undead invaded the realm of the living.
Perhaps the undead belonged to their own realm, but in their lust for power, they invaded the realms of men to seek more meatbags to strengthen their armies and continue to fight against each other.
Theory #5
The undead are actually just a variant of the living.
Perhaps the undead are not so different from the living. Perhaps they have the same humble beginnings, but they were transformed or cursed in some way to live as a different kind of sentient creature. That is often the case of Werewolves or Vampires. Perhaps the different human families in the land, in their quest for power and control, cursed each other (or themselves!) with many plagues and maladies, and each of them acquired mutations over time that transformed them into different kinds of undead: the Liches, the Revenants, etc. They might hate each other for their differences or for having being cursed by each other, or they might simply hate themselves because of their past, or even for their current reality.
Theory #6
The undead are a phenomenon of the world.
Perhaps the game's world created the undead in some manner. Perhaps the artifacts and the magick that powers many anomalies and phenomena of the world have also created the undead. If that's the case, the humans might have tried to use or consume the magick and artifacts that powered their undead existence, and that might be killing them. This is reason enough for them to fight each other.
Those are my theories for the reasons why they fight.