That counsellor will have been a Christian counsellor, and probably an evangelical (see her comment about her 'faith' the client could become straight). There is a huge problem with homophobia in many evangelical churches, which I have mainly seen manifest in gay and lesbian people being pressured into life long celibacy or straight marriages. Its truly disgusting.
Of course, we also know that there is problem with religious people, communities and countries who are homophobic, preferring people to 'transition' so they can appear straight, thus removing the stigma/sin of being gay.
The thing is, if someone says they are gay, there is no harm from them being gay or lesbian. Even in the unlikely event, though I have known it happen, of them later changing their mind. You can change your mind on being gay or lesbain and no harm has occurred at all. If someone says they are trans and wants to medically transition, they are going to become a life long medical patient and have life long consequences. Which is why we need to be sure that person is making the right decision. Especially as we know feelings of GD can be caused by things other than a life long condition of GD. We know if can be caused by trauma and it can be caused by being same sex attracted, and in that case, normally resolves through puberty. We also know that some people prefer to manage their feelings of GD whilst living fully in their actual sex ( so without any transition).
Trans conversion has been lumped in with gay conversion for political purposes, and probably has been argued for by campaigners both as part of their agenda to equate being trans with being gay and to make their affirmation only model predominant, by crushing 'the opposition' ( as they must see it) with fear of prosecution.
Is there even any evidence of counsellors trying to 'convert' people out of being trans? Does this even exist?