As a psychotherapist, working with people who are self-aware is a pleasure. I wouldn’t ever say that to someone if not meant as a genuine compliment.

Although I believe not many of our patients actually are as self aware as they think. I think we as humans often are good in introspection where it’s easy and comfortable to do so, while glaring over pretty blatant cognitive errors in some other parts, and this is usually where problems arise and disorders develop. And interestingly some people seem to think of themselves as someone who’s perfectly introspective but just for some external, unchangeable factor immune to any kind of positive change. Maybe they could feel irritated about the compliment, because in their minds it reinfoces their idea of being helpless against their problems (in the sense of: I already know everything, it’s just not possible to change anything or I would’ve already done that)? I could imagine that’s how I would feel, but of course it’s just a guess.