The thing is, what does being "mentally one gender" even mean? It's not like all people of the same gender have a hive mind.
It's really not hard to understand. You identify as male, female, neither, fluid, etc. It's internal. Most people have a perception of themselves that matches their physical sex. There are distinct differences between men and women mentally that can be measured scientifically with brain scans. Male identifying people in femnine bodies have brain scans that match closer to male identifying people in masculine bodies, and vice versa. I'm sure you know, from living in society that enforces gender roles, what "masculine" like thoughts and "feminine" like thoughts would be without needing it spelled out in minute detail. Pretending to be obtuse about it doesn't change anything.
Yes, gender can be, and likely is, a social construct, but it still exists, but gender isn't just about outwardly matching that construct. A tomboy is not a transman- a tomboy will probably not identify internally as masculine, even if she bucks the gender norms and prefers tools and playing in the mud. She will still see herself as a woman. A transman does not.
There are outliers in every group, so of course not all people of one gender identify exactly 100% the same, and no one ever said they did, but there are trends within those genders that groups of people will identify with more than others. I find this line of questioning ("but why do you even care about gender/what does gender mean?!") more diminishing of our experiences than enlightening. Most people feel they have a certain gender. Those genders tend to have more in common with themselves than those outside of their gender. Gender is not a physical attribute, but a psychological one. Gender exists as a construct, and has for thousands of years. Would society be better if people threw gender out and stopped giving a damn how people saw themselves? Probably. But that isn't what we exist in right now.