Category error

Hey indeedy.

One of the best ways to win arguments is to be so completely wrong that there's no way anyone could feasibly correct you without teaching three entry level college courses in the process. This is known colloquially as a "Shapiro."

The reference is presumably to Ben Shapiro but there are other possible eponyms. A more complex way of stating this idea is fractal wrongness, as one of the commenters on the original tweet points out:

Fractal wrongness is the state of being wrong at every conceivable scale of resolution. That is, from a distance, a fractally wrong person's worldview is incorrect; and furthermore, if you zoom in on any small part of that person's worldview, that part is just as wrong as the whole worldview.. . .

The term "fractal wrongness" may also be used to refer to someone who is consistently wrong on nearly everything they predict or claim. Repeatedly failing predictions is one of the best ways of revealing fractal wrongness, because while an idiotic worldview may work in someone's head, it can be seen failing when actually put to the test. Hilariously, people who are consistently wrong tend to be quite confident in their position while championing it.
Fractally wrong people are often immune to the stopped clock rule because they are not exactly stopped clocks. More like clocks losing a random number of seconds a day, in the wrong time zone of the wrong planet, in the wrong solar system.
Debating a person who is fractally wrong leads to infinite regress, as every refutation you make of that person's opinions will lead to a rejoinder, full of half-truths, leaps of poor logic, and outright lies, which requires just as much refutation to debunk as the first one—kind of like a recursive Gish Gallop, where each point both surrounds and is surrounded by an equally wrong argument. It is worth noting that being fractally wrong can be handy for the losing side in a public debate, since you are likely to leave your opponent looking baffled and unable to deal with each level of wrongness. 

The category error in this case would consist of trying to engage with these people rationally. It isn't worth it.

Next: Common category errors made by people who might be worth debating.