Well, m'self for one. Any number of other trans people I've met in person and online.
As for the why: one of the really core issues trans people face is invalidation of our identities, both overt and subtle. Marking us off as "other" in situations where it's not relevant is a part of that -- even non-bigoted folks often consciously or subconsciously perceive us as not really who we claim to be, and while they don't wish to antagonize us directly, they can't quite bring themselves to take our claims of being men or women at face value, at par with those of cis people. (Not even getting to what nonbinary folks face there.)
One thing some of us have observed is that using "trans-" as a prefix is a way to keep us comfortably-other, mostly in a subconscious way. Would you expect to ever see someone regularly and preferentially referring to Alice as a blondewoman, or Sally as a fatwoman, or Cheryl as a blackwoman? Not barring some kind of long-term shift in colloquial English use.
Basically, for some trans folks "transwoman" and "transman" just come off as fenced off from "woman" and "man" in a way that amounts to a sort of compromise, one we aren't comfy with. This is not universal; even for people who have that pet peeve, it's not something they always bring up at every juncture, but it's probably worthwhile to know about.
one of the really core issues trans people face is invalidation of our identities
One of the interesting sub-issues here is whether one naturalizes gender or regards it as a construct. That is, a person might defend their right to be regarded as female or male despite their birth anatomy, on the grounds that this has always been their true gender; or they might defend it on the grounds that gender is a person's choice. I see much greater cultural receptivity to the first idea, and yet I also see fantasy, socialization, and escape from contingent gender norms playing a large role in why people want to transition.
If it's worth saying, but not worth its own post, even in Discussion, it goes here.