Perhaps it hasn't reached the sophistication of a debate.
Tony 1 said "I have already stepped over the line ", you replied "No, you haven't,", Tony came back "Yes I did step over a line" and suggested that your own intervention wasn't helping.
You responded "No, I can't agree with that" and advised Tony to "be careful". So, on reconsideration, perhaps it was more of an argument than a debate. But having met neither of you, it's difficult to be certain. You say it's not a debate, perhaps Tony thinks that's debatable?
Anyway he has coined a memorable phrase "ugly knife fight that one sees in the loathsome cesspool".