This is absolutely right. I find that disagreeable people, who rarely consider themselves to be disagreeable, find me to be disagreeable because I do not allow them to bully others or me. One of the most important skills for academic leaders is, IMHO, the ability to tolerate conflict and to manage it for the good of the department and the school. Running away from conflict, which, sadly, far too many academic administrators do, leads to toxicity and bullying.
I still remember an incident when I was a chair when the department bully (who thought of himself as much beloved) tried to get in my grill about something and actually threatened to get me fired. He didn't get what he wanted, either with regard to his specific demand or to get me fired. Bullies hate it when someone stands up to them but it really is incumbent upon chairs, deans, VPAAs, and presidents to refuse to play nicely with bad actors.
If you are a department chair and reading this, please do take anthroid's words to heart.
Yes, this is so wise. I think it can be hard to stand up to people like this, especially if they are doing other things for a department (i.e., pumping up publishing/grants numbers). But it's absolutely necessary.