The article states that Aristotle and many modern philosophers agree that a desire for payback is a fundamental part of anger.
I questioned it too, thinking through a bunch of different scenarios.
The biggest counter example that popped into my head was being angry at my kids for doing typical kid stuff.
I'm not trying to get "payback" or revenge, right?
When I paused and reflected on it, I'm not so sure. Why do I raise my voice? I want them to feel bad, theoretically so that they learn to not do whatever it was they did. Is me wanting them to feel bad wanting payback? I guess you could argue that it is.
Whenever I get angry, it's very action-oriented. I stew on what I'm going to do in response to whatever made me angry. After I calm down, I can recognize how irrational most of those thoughts are.
My brain doesn't function well when I'm angry. The thing that I've learned, and it's been a hard lesson at times, is to not react. Those feelings of revenge and payback etc... make everything worse.
Especially when I really look back on whatever situation made me angry. Once I'm calm, I'm able to see what part of the situation was my fault. A lot of times, it's an embarrassingly large part, and the fact that I was a jerk in some way is hard to admit.
It's a lot easier to just externalize it all, get mad at someone else, and contemplate ways to "get even".