Explain transgender

I'm not trying to be rude, but as hard as I try, I just don't understand. What do you mean "assigned gender"? If someone's gender is "assigned" to them by their genetics, and you believe they were "supposed to" have a DIFFERENT gender than they were actually given-- what does that mean? Like their SOUL has one gender, and their body and genetic makeup and hormones are a different one? I have tried so hard to understand it, but it just doesn't make sense to me. Like, how I look at it is, you are your gender, male or female, which is based on genetics, genitalia, etc. And the way you act or the things you like shouldn't be dependent at all on genetics or genitalia. Like, why can't a dude be a dude with a penis, and like to wear pink dresses too? Why must he automatically be assumed that he wants to be a GIRL just because he likes to wear pink dresses and makeup? I don't understand why we have to say that just because they like those things, then they must have meant to be a girl but accidentally wound up with a penis and testosterone?? No, he's a male, who likes dresses and makeup, and maybe even guys. I just don't understand what this whole "supposed to" talk really means...

To me it just seems like self-hate or looking at your body like it's "wrong" and it shouldn't be that way. I don't like that notion at all.

Anyways, please explain the whole "assigned gender" vs "real" gender thing.