the more labels they have, the more unique and/or complete they feel.

That sounds completely bonkers to me but you might be right.

if my trans brother feels better because his label is now male, that's fine

No, of course if you don't like the body you have and you want to change your "gender-defining" features, you should. It's a bit like changing your haircut - although more impactful. You didn't like your looks/body before, so you changed it and now you feel better so that's perfect!

Before I learned about the LGBTQ community, I thought of gender as something you were born with and that described your body type: masculine or feminine. Aside from that, I don't and never believed that it defines what kind of person you are, it only defines a part of your looks.

Now with the community there are people who describe themselves as non-binary or agender and again, I'll totally respect that. However when I tried to think about what my gender really was, I started to realize that the whole concept of gender didn't really make sense to me. What does it really mean to be non-binary? Heck, what does it even mean to be male or female? If it's not just your body-type then what is it? Why do we need it? Isn't it easier to not assign any genders at all? Just be who you want to be and love who you want to love!

I think a little bit it’s just that people typically like labels

It's not just a question of liking. Human minds work setting categories.