There is no denial of anything. There is factual reality.
Something opponents deny.
A man is a man and a woman is a woman and there is nothing that changes that.
Labels are labels and their use changes over time. Fact. Otherwise, the term gay then has never meant homosexual. And for that matter gender does not mean sex under that logic as well, since it was never used as more than a euphemism before it became a synonym sometime in the 18th or 19th century.
You are correct that the biology of a person will always be what it is. But that doesn't mean that it is what you think it is or want it to be. Genetically speaking, there are males (XY) born with vaginas. Do you claim them a man or a woman? Please don't quibble with the "they're an exception" weak ass argument. With that argument, all homosexuals and transgenders are an exception. But I digress. Regardless of what the reality of the body is, the label can change. Man and woman can be changed to apply to something else, much as gay has done. So could male and female for that matter. As to whether or not something could be going on with our bodies and whatnot, that we never noticed before, I draw your attention to women miscarrying. For the longest time, we thought that a woman who did not get pregnant or rarely got pregnant, had fertility problems. Now we have the means to detect the more subtle signs of a miscarriage (and a stroke and many other things we could not detect before), and have determined that many women miscarry far more than they are aware of, having it happen so early in the pregnancy that they never know they are pregnant. Now if we could have been making that kind of error before, then there is no reason not to have been mistaken as to the difference between sex and gender (or whatever labels you might wish to use)
Some people have a mental disorder that makes them think that they should be something different than what they are, and some people are hoping onto it as part of a social contagion (especially kids). None of that changes anything.
Claiming something to be a mental disorder simply because it changes your worldview or you don't like it doesn't make it so. Especially when the actual professionals say otherwise. There are plenty of things that we used to claim as mental disorders, or worse, that we no longer do. Left handed used to be a mental disorder a long time ago, if it wasn't claimed as demonic possession or just plain a choice to sin, as homosexuality and transgenderism is claimed by many today.
Mental disorders reflect the anxieties of the era. A study of the Diagnostic and Statistical Manual of Mental Disorders (DSM) reflects a constantly
listverse.com
That doesn't mean that people with these issues should be targeted for mistreatment for just existing.
On this we can agree. And ultimately there is something wrong with a person who is transgender INSOFAR AS, if there is nothing wrong then there is nothing to correct. That is why homosexuals don't need anything done to them (despite opponents' claims). All of a homosexual's stress and anxiety comes from outside of themselves. A transgender's GD comes from inside. It wouldn't matter if all of the US went to wearing "women's clothes" (which is totally a social construct since all clothing types have been worn by both sexes throughout history), the social construct of clothing styles is not the source of the GD. It might be a method for relief of the symptoms, but it's not the source. The fact that their two aspects are mismatched to a degree that it causes stress and anxiety, means that there is something wrong.