A good moderator is always wrong. Well, that's the experience I have, and I've seen it in all places where I held the mod badge the past 20 years or so. It depends on the person in question though. Some people can easily be turned over by talking to them and negotiate with them, others can best be kicked off the site immediately. The trick is to find which category an abuser belongs to. Those who break the rules out of ignorance are mostly easily filtered out.
And once I deleted a post as a mod as it was a site were advertising was not allowed and where I even politely explained the rules about that a new post came that I was acting like I owned the place. Sounds to me like you blame a cop for acting like he owns the road when he gives you a ticket for driving through red light, to be honest. Rules are rules, and I merely did my duty. No ads = no ads. He got an official warning for that action, and when he finally understood I was actually part of the staff, he quit.
Those to whom a moderator acts quite often will deem everything you do wrong. Some people make it easy though. I once warned a user who was harassing other users and he replied with "To moderator Jeroen! Why don't you go f---- yourself?" I love it when they do that. That justifies an instant ban. I wish they all made it so easy for me.
Another lesson I learned over the years. Those who cannot accept there are rules and that there are limitations how far you can go, and who are quite often walking the edge of not allowing a moderator to push the ban button, are also the ones who complain most about moderators. It's a pattern I've seen that is rarely different. Gives one something to think about, eh?