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The problem here isn't necessarily labeling being LGBTQ+ as a mental illness, the problem is the assumed solution. I'm not a psychologist or a psychiatrist, nor have I talked to one at length about gender or sexual orientation, but I do know that having an illness does not imply that the illness needs to be "fixed," only the discomfort associated with the illness needs to be addressed. Sometimes "fixing" a problem is the best solution (e.g. a broken bone, depression, etc), and sometimes accepting a problem is the best solution (e.g. blindness, autism spectrum, etc).

You can only be cured of a mental disorder if you want to be cured. My understanding is that most LGBTQ+ don't see their divergence as something to be cured, so whether we classify it that way is irrelevant, the best treatment here is social acceptance and maybe physical alteration (hormonal therapy, surgery, etc). That has been proven time and time again, and unless someone comes up with a better solution, it's the prudent option to take.

So I don't see being LGBTQ+ as a "problem" to be "solved," rather I see intolerance of LGBTQ+ people as a problem to be solved. LGBTQ+ people don't harm themselves or others by being the way they are, but intolerant people absolutely harm LGBTQ+ people by treating them the way they do.