"Are you calling me a liar?"

Solution 1:

No it would not best be described as ad hominem, as it is not attacking you at all. It isn't even making a statement, as it is asking a question.

The best description of this fallacy (assuming you did not call actually call the other a liar) would be a Red Herring. The other guy is shifting the grounds of the discussion from the original argument to a new one that is presumably easier to defend.

If you think the accusation was merely outrage at being disagreed, then the closest fallacy to that would be argument from authority. He is considering himself the authority in question that must be accepted ipso facto.

Solution 2:

The "formalisms of rhetoric" can be a pain in the tuches, to be sure. Kind of like the Latin names for flowers and trees and diseases and so on. They can be helpful, however, whenever you're interested in spicing up your communication with little rhetorical flourishes here and there. Some people may use them simply to impress others, and that's OK. A better use for them is to achieve better precision, as well as memorability. A good metaphor, analogy, or other figure or trope can help people better remember what you say.

As for the "Are you calling me a liar?" locution, it most definitely can be voiced in a bellicose manner! I wouldn't call the locution an ad hominem, however; rather, I'd call it a reaction to a perceived or inferred ad hominem (i.e., an attack against the person and his character). Rather than being a rhetorical figure or trope, it is probably better described as evidence of a truculent disposition or temperament. Some folks are overly sensitive to a perceived insult. A simple and innocent "Are you sure about that?" can elicit a "Are you calling me a liar?" from them in a nanosecond!

Solution 3:

In an argument between debaters where observers are judging the outcome, this might be called poisoning the well, describe in Logically Fallacious by Bo Bennett (and also Wikipedia):

To commit a preemptive ad hominem attack against an opponent. That is, to prime the audience with adverse information about the opponent from the start, in an attempt to make your claim more acceptable, or discount the credibility of your opponent’s claim.

One could say that, by making the accusation about lying before responding to the argument that has been made, the well has been poisoned, and diverts attention away from a weak direct response.

Related is the just because I say so or appeal to authority fallacy, which apply even when there are no outside observers to the debate. These are described by Bennett thus:

Refusing to respond to give reasons or evidence for a claim by stating yourself as the ultimate authority in the matter... “Just because” is not a reason that speaks to the question itself; it is simply a deflection to authority (legitimate or not).

It can also be described with some of the more fundamental terms of rhetoric.

Ignoring the issue (ignoratio elenchi) (Wikipedia) is a catchall for many debate tactics, including this one, where the speaker is changing the subject to "Let's talk about what you think about ME" instead of "Here is where you are wrong about what I said".

Your example is a peculiar one, because it might be taken to implicitly accuse the opponent of being the one who changed the subject.

It also becomes a bald face appeal to emotion (pathos) over credibility and logic (ethos and logos) when the object of the debate is to sway observers. Pathos, ethos, and logos are referred to as the modes of persuasion, recognized by Aristotle in his On Rhetoric.

This is clearly an attempt to flip the switch from ethos and logos to pathos

So you might consider this to be a pathetic attempt to change the subject. :)