Like I said I have to deal with the same issue thanks to mountain lions. I don't think it's a valid reason, it's a supremely selfish and shortsighted one.
The regulations on wolves are different. You can only get permission to use legal force on a case by case basis if they are attacking livestock (or if you catch them in the act).
You can use force against a wolf attacking a working dog or yourself, but not a pet.
In all other cases, you must use non-lethal detergent methods.
I live in California so the only minor difference is that you can use lethal force if a mountain lion is attacking a domestic animal but the CDFW will be on your ass and you better be sure it was the only option or you'll get prosecuted for poaching. (I just shoot a shotgun into the air which scares them off)
Otherwise you need a depredation permit that are "must issue" if you have evidence of a mountain lion attacking your livestock but only one in ten applicants are granted a lethal depredation permit. The rest must use non-lethal deterrents because lethal force is only authorized if there's a genuine threat to public safety.
For a rancher or someone living in a rural area, lethal permits are rarely issued. In several parts of the state like the Santa Monica and Santa Ana mountains permits are no longer issued at all.
In a different post, someone mentioned that livestock lost to wolves receive compensation. Is it the same for mountain lions? That seems like an excellent way to reduce requests for "depredation permit". (LOL: What a term!)
No, but mountain lions aren't pack hunters that can really threaten commercial livestock. They usually only predate solitary animals on smaller farms and even though it's far more traumatic for us than a rancher losing one head of cattle out of hundreds, we don't want to kill them. The state doesn't have to bribe us. They're basically sacred in this state and some like P22 even become mini celebrities.
(The term depredation comes from military attacks on helpless villages so the term is very fitting, both in terms of the mountain lion attacking livestock and humans hunting mountain lions)
You can use force against a wolf attacking a working dog or yourself, but not a pet.
In all other cases, you must use non-lethal detergent methods.