I do some beaver trapping. They're neat critters, so I mostly leave them alone if they're not bothering anyone. People get mad when they're chewing down $1000 ornamental
trees or building (and rebuilding on a nightly basis) dams that flood their only road to their field that needs to be harvested.
I'm well aware that there many effective ways to deal with beavers other than trapping them and killing them, but by the time they're causing problems, people want them gone like right now, and I can get them out in a night or two.
Most of the time, people don't know they're there until they start causing problems. They move in during the spring dispersal, but don't starting doing a bunch of chewing until the fall, and by the time they start chewing, it's time for immediate action.