I basically agree, but I think the point is stronger if framed differently:

Some defects in an argument are decisive, and others are minor. In casual arguments, people who nitpick are often unclear both to themselves and to others whether their objections are to minor correctable details, or seriously undermine the claim in question.

My impression is that mathematicians, philosophers, and scientists are conscious of this distinction and routinely say things like "the paper is a little sloppy in stating the conclusions that were proved, but this can be fixed easily" or "there's a gap in the argument here and I think it's a really serious problem." Outside professional communities, I don't see people make distinctions between fatal and superficial flaws in somebody else's argument.

In summary: I think your post is a good one but with minor correctable flaws.