Thankyou for mansplaining that to me.

If you say you disagree with something lets say it's the concept of mansplaining it's self.
And no carefully you articulate your point against it the answer is "thank you for mansplaining that to me". What fallacy would that be an example of?

This isn't necessarily a fallacy. It could be a sarcastic/semi-serious remark, a serious observation (some men do mansplain), or an attempt at dismissing an argument (fallacious).

In this case the implicit assumption is that because person 1 is male, they have no right to comment on an issue pertaining to person 2 (who is presumably female). 

That would normally be considered ad hominem (circumstantial) but as I wrote above, one would need to see if there is actually an argument being made in order for this to apply.

I think everyone who answered so far has contributed some good insight to this. Without repeating what was already written, I would add that this is a major problem in communication when others assume bad intent. It is so important in good communication to offer charitable interpretations and ask for clarification if unsure.

Regarding disagreeing with the concept of mainsplaining, I would be curious where the disagreement is? That no men are ever condescending or patronizing? Or perhaps that responding in a condescending or patronizing does not correlate with a particular gender? Or that correlation is not causation and men are unfairly demonized by this? In doing some quick research of the scientific literature, I could not find anything that supports the idea that men do this more than women, although there does appear to be studies that show that those in power do this more often, and it is more common for men to be in power. But is this fair to associate the trait with men rather than those in power? Not sure, but something to think about.

As I see it, it's just unsupported claim. She accuses you of being condescending and as I see it it's an accusation of the way you explained it. Actually I didn't know the term "mansplaining" but in wikipedia it says "(of a man) to comment on or explain something to a woman in a condescending, overconfident, and often inaccurate or oversimplified manner". It implies there is arrogance behind the explanation (which is psychogenetic fallacy ) but apart from that I would ask specifically whether my explanation was found just condescending or/and false. 

Since the retort is directed at you personally rather than your explanation it qualifies as an ad hominem (to the man) fallacy as a guilt by association subset. The strength or weakness of your claim is not an issue, but the assumption being made is you’re a man who arrogantly assumes he has the best and most correct answer to everything all the time (and thus a turn off to women).

The proper response to the allegation of mansplaining is to correct the error and say: “Mansplaining is a pejorative ad hominem term meaning for a man to comment on or explain something to a woman in a condescending, overconfident, and often inaccurate or oversimplified manner. You got it wrong, sister.

" I’m a woke self-identified Hispanic Caucasian Black Asian identificarian eunuch in gender-transition, not yet fully transcended, but non-binary, cisgender queen-king, quoiromantic, and sometimes cupiosexual paleface with the amalgamated brown and red skin of a Native American Indigenous apparition. I wasn’t mansplaining, I was eunuchsplaining. Got it?”

That should end the discussion and you can move on to something important, like the golf scores.