That depends on the definition of 'it'.
even though it has no 'right' answer
Does this refer to the PROBLEM, or the PERSON?
If it's the person, and they have no explanation behind why they think I'm wrong, they're ignored immediately. Yeu can't just go "Yeu're wrong" and leave it at that and expect anyone to think yeu're not an idiot.
If they can prove that I'm wrong but just don't happen to have any idea whot the 'right' answer should be, I'll concede defeat, but continue on as I was until a better alternative is presented. If they have failed to present an alternative, and I have yet to find one myself, then there's no point changing my ways at that time, despite being in error. "Fairly close, though flawed" is still better than "doing nothing", at least in most cases.
If they pressure further to stop whotever while lacking an explanation, then they're ignored. Otherwise I don't care either way.
If the person says I'm wrong, and there ISN'T a right answer to the problem to begin with, then they're just stupid for trying to think of whot's clearly a shaded issue as black and white, and I have no reason to waste my time further with them.
Overall, I guess it depends on whot yeu mean, since yeu worded this very, very poorly. Most come out to the same answer, however.
EDIT: Now if they were RIGHT, and I was WRONG and they had PROOF of my being wrong, with clear evidence or logic to support it, and they had an alternative or I was able to figure one out after learning such, then I'd just simply change my mind or ways to match the correct information. We don't know everything, even I don't. As new information becomes available, yeu have to be capable of adapting to new knowledge. As such I'd hold no harsh feelings in that scenario at all. If I didn't have cause to believe I was wrong, I probably wouldn't've figured it out on my own, as that would require needing to look closer on the matter, and without reason to do so, it's unlikely I ever would've until it was mentioned to me.
That's not whot the question was though, but it's out there just because =3