I think the problem is "who gets to be verified?" Why can't I be verified? The implication was that verified users were special in some way (maybe just in a Sneeches "stars upon thars" way), and so giving it to admitted Nazis and white nationalists was seen as saying they deserved to be special. And then taking it away made them and their supporters feel they weren't special anymore.

Right, its all about how people outside of Twitter perceived the checkmark. Twitter made it worse for themselves, because people are just going to find sexist/racist tweets from verified people and get Twitter to un-verify them via negative clickbait PR.