The main problem with 'trans rights' arguments is they are completely anti-scientific. They use the opposite of the scientific method.
Instead of looking at evidence and drawing conclusions, they have started with the conclusion that they want (men can become women, women can become men), then worked backwards trying to disprove anything that shows this not to be true (pretty much everything).
One of the problems with this is that you have to adopt more and more extreme arguments in order to account for all the inconvenient facts. For example: religious fundamentalists who believe that the world is about 6000 years old have to invent ludicrous tales to explain dinosaur skeletons, or tree ring data that shows the trees were alive 14,000 years ago, or pottery made more than 20,000 years ago.
It's the same with trans ideologists. Their beliefs have no basis at all in truth, so they have to invent 'female penises', and 'same gender attraction'. They claim that if a man has sex with a 'transman' (eg a woman) this man must be gay, even though it was a mundane heterosexual act. They have to claim that sex is 'assigned at birth' even though nobody ever remember assigning their baby as anything, they just had a little look (or more likely knew months in advance of the birth). They have to deny all scientific evidence when it comes to sport as admitting that men are not women would destroy the whole concept, so they demand that everybody denies the evidence of their own eyes and experience, not to mention literally thousands of years of data. They have no arguments at all about why it is impossible to be 'trans race', but they know it is a horrifically racist idea, so they have to quickly scream 'racist' at anyone who questions trans ideology in order to cover their own racist beliefs. They have to shout 'no debate' because deep down they know they will lose that debate.
Basically, the 'main flaw' in the 'trans rights' argument is that the whole thing is a pile of shite.