This works similarly to paradigms in science. Most of the time people don't actually define paradigms; it's implicit in the general experience of being a researcher. People similarly have a commonsense understanding of what hate, bigotry, and racism are. This works fine when everyone agrees, but once a field reaches a crisis, once you have a political climate so violently polarized, it stops working to appeal to people's basic intuitions. People no longer agree on the most basic things. You have to start calling out specifically what the other side is doing and why it's a bad idea.

Simply calling someone "hateful" is an emotional argument at this point, and hurting discourse.