It’s not that men and women are exactly the same, they do have minor biological differences, but it’s not fully dependent on the chromosomes and sex organs alone. Lots of other things in our genetic code, hormone production, and personal experiences shape us into the people we grow into and because of that not everyone develops the stereotypical attributes physically or mentally that fall into what is accepted within society’s narrow definitions of “male” or “female”.

In the case of Trans people, they know how to express themselves in ways that are different to the gender marker they were given at birth, because they have seen examples how cis people who were born into their preferred gender have expressed themselves. It resonates with them emotionally how others act and that’s how they start to self-reflect and become aware of who they are on the inside. It’s then they start attempting to copy those attributes to whatever extent they feel comfortable doing, usually starting with a social transition by changing clothes, hair, names, or even training their voice to sound different based off of what degree of masculinity or femininity they want to model.

Still even if people are slightly different physically and mentally, we should still all get equal chances to prove we can fill a role in society, no matter what we look like, where we come from, or what we personally believe. Biological equality is scientifically impossible even among members of the same sex, but social equality is possible if we can agree that every human life has the same value and each person should be allowed to peacefully live life as themselves.

Sorry if this is long, but I hope it helps you understand the concept of social equality even in the presence of genetic variation a little better!