Well, obviously a Predator would really not want to die and they do want to self-preserve themselves. But at the same time, by the very nature of what they are and what they do is travel to different worlds and fight with their toughest prey. They remind me of Klingons "today is a good day to die " !
they don't fight prey. no one fights prey.
they hunt it.
seek, track, pursue, kill, collect, go home. taunt in the middle if the mood is proper (P2 teasing Harrigan with his friend's death, P1 pushing Dutch around the forest with his gun in the unfinished scene).
P1 was getting even with Dutch for spoiling the hunt and forcing him into contact.
P2 had fun luring Harrigan into fear, while always avoiding the contact itself.
nobody of those two was or wanted fighting. fighters are in AVP. we spoke about different species (one of them plagiarized from another).