I'm as accommodating as the next guy, but there are two things that I cannot abide on my property:
1) yellow jacket or hornet nests
2) venomous snakes
It's just too damned easy to accidentally (or drunkenly) stumble upon, and get seriously fucked up by, either one for me to peacefully coexist with them.
I'm also not a fan of house centipedes. Yes they're nice little predatory critters, but they lack boundaries, and they also enjoy leaping at me from the ceiling.
Spiders unfortunately must die as well, unless it's a particularly large one that is amenable to capture.
1) They hatch out egg sacs, and then the babies climb up to the top of my dining room chairs and cast out silk lines in the hopes of catching a breeze to some distant land.
2) They also know no boundaries, and will sometimes try to join me in bed.
If I could, I would gladly set up a treaty with some of these predatory arthropods: They can patrol the house for unwanted things, provided that they do not ever climb on me, they stay out of my bed, and that they remain at least 4 feet from me at all times, unless there's a wall between us. There is also to be the understanding that if any of these provisions are violated at any time, or if they bite me for any reason, their existence will abruptly and violently end.