Mentally? No, it's dumber than that, gender was coined as a "social construct". Eunuchs are considered a "third gender" by "queer studies". They use gender and sex interchangeably to make it seem more legit, but it's all sophistry.

Sex is binary and has a biological background (chromosomes, gonads, hormones, and genitals), you can't "identify yourself as having certain chromosomes", you have them or you don't. Gender encompasses things like: gender roles, gender identity, gender expression and has a social background, which means its criteria is fluctuating all the time. It originated from feminist theory since it framed women as a sociopolitical class, resulting in gender and queer studies

The mismatch was called "gender identity disorder", it was replaced by "gender dysphoria" in the DSM-5, under the following argument

DSM-5 aims to avoid stigma and ensure clinical care for individuals who see and feel themselves to be a different gender than their assigned gender. It replaces the diagnostic name 'gender identity disorder' with 'gender dysphoria', as well as makes other important clarifications in the criteria.

Note that they also changed the definition so that "not all transgender or gender diverse people experience dysphoria".

There are treatments for gender dysphoria, there aren't for "queer" people since is considered an identity, that's why they have to present it as a discrimination problem, the catch is: you can make it all up and people can't disprove you or else they'd be called bigots and be deplatformed