Yes. In a debate everything you say should be backing up your thesis, otherwise you are just muddling things yourself.

If what you say is supporting your point than I am going to poke at every hole and weakness I can find in order to weaken your overall thesis.

Debates naturally grow and shrink in scope. The first few messages are large as people bring up all their evidence. Then the debate shrinks as both sides begin to concede or drop points that become irrelevant. At the end a good debater would go back through what was said and synthesize it back into one overall large narrative.

At what point does it become nitpicky? I have to figure out which things you said are open to criticism and which ones aren't.

What you want, a debate where all we do is "approach the argument you're making" is what you see in every presidential debate. If you enjoy that, more power to you, but you aren't learning anything or discovering any truth about the world.