Why call it "gender dysphoria" when it's clearly "sex dysphoria"? Transgender vs Transsexual

MtTs get offended if you use the term "transsexual" instead of "transgender". These people claim gender is in the brain.

If they wanted to alter their brains to match their body, wouldn't THAT be transgender? That's not what they want, though.

They want to alter their genitals, their biological sex, so transsexual seems like it would fit more. They are unhappy with their private bits and want them altered, rather than seeking out help to fix their mental problems.

It IS a psychological issue, without a doubt, but if they wish to claim otherwise it would make more sense for this group to adopt and embrace the term "transsexual".