There are several points here that seem entangled, but I'll try listing them separately.

First, it is a desirable quality to be able to work out what one did wrong from minimal evidence, or repeated experimentation.

Second, it seems to me that rationality is strengthened by the ability to joyfully accept contradictions and corrections. A view that sees a downvote as a sort-of public humiliation is probably too sensitive.

Third, politeness is costly, in several ways. Most relevant to the others is the time cost of writing a reply. It often takes much longer to instill clarity than it takes to display confusion.

Fourth, as the benefits mostly accrue to the corrected, and the costs mostly accrue to the corrector, it is not clear why we should expect such correction to be the norm instead of virtuous on the part of the corrector.

She might become so upset she won't return here again.

LWers differ in how hard they want LW to be on its new users. I tend to be softer than, say, Lumifer, but I am not certain that this is a bug instead of a feature. There are people we don't want to discuss things here on LW, and that sort of reaction may be a decent filter.

...it is only going to hurt the other party... a downvote is a sort-of public humiliation

Oh, dear. HTFU already. People who think of downvotes as hurtful and public humiliation really shouldn't venture into the wilds of 'net forums.

Er... That was my point.

I think the point is that you shouldn't conclude "that you're confident you don't want this person in our community" just because "the argument is so moronic".

(Because there's too much noise with individual arguments to deduce a person's general competence.)

In other words, yes, downvote the comment - not the person.

Also, consider the possibility your own judgement is affected by tiredness or mind-murder.

I guess you are talking of conditions in which someone makes a downvoting decision. But then underconfidence is also possible, and also a pathology, making one unable to act on a correct judgement. This point might be a reason that The Sin of Underconfidence is a prerequisite for Well-Kept Gardens Die By Pacifism.