What is "mental gender" anyway? Does every boy who like sparkly stuff be forced to take estrogen? He's mentally "a girl", right? Does every girl who cuts her hair short have to be on Testosterone? Good work, we have brought back gendered stereotypes.
No, each person can determine on their own what gender they should present as; nobody is saying that doctors or parents or whoever should look at people's interests and decide that they must be trans.
A lot of TERFs really enjoy accusing trans people of supporting gender stereotypes, but this is not something that many actual trans people do.
So your definition of 'man' (or 'woman') is "anyone who calls themselves a man (or woman)". Is that right?
If so I think there are obvious problems with such a definition.
Essentially, yes (I don't think people should call themselves the wrong gender in bad faith, but that is not something that happens often for a variety of reasons).
What problems are you referring to?
What's to stop a person with a penis calling themselves a woman to get around gender equality quotas? Or gain access to scholarships for women in STEM?
And then there are the philosophical problems around what exactly it means to 'identify' as anything...