It's more like "this is irritating the fuck out of me and I'm done with it now." It may or may not be personal.

Either "I believe in you. You can do it!"

or

"I don't have the time or crayons to explain it to you right now and you would probably eat the crayons."

It would heavily depend on the context, I think. The biggest question that would need to be answered is, is the other person engaging in good faith? Or is he trying to troll?

If he's trolling, he may be trying to do a Gish Gallop, where he constantly brings up vague and untrue points in the hopes that you eventually burn yourself out trying to figure out what he's talking about.

If he's not trying to troll, then maybe he thinks you're trying to sea lion, where someone constantly asks questions in the hopes of burning someone else out.

Otherwise, if it's in an educational context, he's expecting that you can figure it out and that doing so will help your comprehension of the material. It's probably not this.

Based on what you write, I would lean toward that the other person is not engaging in good faith. That being said, without seeing the full context, I cannot fully say that it's not that you're the engaging in bad faith (people do tend to romanticize their one side, after all)

You officially exhausted him with your exchange. I become equally dismissive once I'm 4 comments back and forth with a stranger.

In this case, I think your interpretation (“I’m just gonna disengage while trying to save face”) is spot on.

I can see it going the other way, though. I might finally respond with “figure it out for yourself” after a sealioning pedant has exhausted me, and I would rather end the conversation than explain my point for the third or fourth time.

The flipside is that unless you're hired to be someone's teacher, nobody is obligated to explain things to anybody else. There are also "the journey is the destination" type questions where the answer doesn't matter as much as the process of figuring it out yourself. Like science experiments in school where the answer is already known and the point is to teach kids certain ways of thinking or how to use certain tools. So yeah, there are legitimate reasons to say that, but a lot of the time it is indeed a cop-out. And your example is absolutely one of those times.

There's only so much time in the day. And far too easy to waste it arguing pointless things with random strangers on the internet.

In this case, their motive does not matter. They did you a favour shutting it down before you wasted any more time thinking about something that does not matter at all.

Yeah, that's them saying they are done with the conversation.

That said, I've seen people open with it as an argument here on Lemmy, so what you went through seems tame.