It's a combination of things; mostly a form of tribalism and a sense of power. That's not necessarily a bad thing if you can moderate yourself in addition to the community, and if you recognize your own cognitive biases. These mods, however, don't. There's no incentive for them to look inward when they all pat each other on the back for destroying their perceived enemies.
Think about it, though; what are the requirements of being a mod? You're generally required to be available quite often, and you're doing it voluntarily. What kinds of people fit that description? Most of the time it's someone who loves the thing the forum is dedicated to, is likely unemployed, with little sense of personal empowerment in their lives.
Not all mods are like this, obviously, but I would imagine it's fairly common, and it explains a lot. Take Ryulong. What does he do all day? Edit Wikipedia (not modding, but it's a similar situation). Why? Because it's the only thing he has that gives him a sense of power. It's the only 'contribution' he's yet made to society, so he guards it zealously, no matter how useless or pointless it might be.
People are literally psychologically biased to believe certain things about themselves and the world. These tyrant mods probably genuinely think they're doing the right thing by shutting down dissent or questioning. They have no problem with exercising their power like they do because there's no immediate engagement with the person they're banning. The nature of the internet dehumanizes their community for them.
The best moderators are those that actively engage with their community and know that it's not for them specifically. KiA has some of the better mods I've seen for the simple fact that they don't shut down dissent. They understand the community, and they got there by creating a dialogue-friendly area for us.
Anti-GG mods don't have that, because they're not about dialogue. They're about pontification and indoctrination. Anyone who threatens their sense of power in their own sub has to go, because it's perceived as an attack on their own self-worth.