How should people be called out?

I'm wondering about this because someone "called me out" on a reply, but I decided to, after replying and attempting to clarify the situation having been met with a snark double-down, just reply sarcastically and block them.

Was that appropriate? I mean the whole interaction.

I think the initial reply, the so-called "call out", was already inappropriate, but I do think the user was interacting with me in good faith. Most of the reply was demeaning and a little insulting, but I do think that it came from a place of frustration more than anything else; the latter half of the text was more meaningful, and I think actually provided an opinion on the subject at hand. I think it was a bad take, in my opinion, and phrased in an overly confrontational way, but it was a take, and that's good.

My reply was constructive, I think, but I did add a particular line criticising the framing of the "call out"... And, well, what I got in reply to that was just a double-down and some insults.

Should I not have added that line? Maybe. I guess so. It was an opening, but I felt compelled. In retrospect, it might've been better to let it go.

Should I have tried to keep the conversation going? The initial reply was in good faith, I think; the second one was definitely not, and it wasn't constructive in the slightest.

I feel conflicted, and I don't think I have an answer yet.

I wore my brown suit, today.