I think my very first impulse would be to withdraw to have some time for myself to analyze the situation and come up with a plan to follow. I would definitely try to get to the bottom of things to try to work things out.
I would be very concerned why the question came up at all. Is it about me or about them? What signs are there for this kind of a question to come up? Has anything changed? Might there be misunderstandings, miscommunication, something I/they have done that has brought about doubts? There might be some underlying problems that have been ignored either by me or by the other party.
I would try to stay as calm as possible, considering that this came up after an argument. It's so easy to start picking at it in a negative way and make things worse. However, as much as I do hate conflict and arguments, I find that sometimes things just have to get a bit over the top in order to relieve the pressure that might have been going up for quite a long time.
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