There's a difference between loving Sushi and being indian than being transgender.\
Here's a simplistic overview of how it works.
Some people are born male, and feel/have the brain of an average (or not so average) male.
Some people are born female, and feel/have the brain of an average (^) female.
Some people are born male, and are attracted to females, and vice versa.
Some people are born female, and are attracted to females, and vice versa for the opposite gender.
Just as sexuality isn't a choice, just as it is an innate part of who we are, gender applies in this manner. Some people are born male and feel male, some people are born female and feel female, some people are born male and feel female (and vice versa).
To equate this to the simplistic dogs view (after all, dogs don't pray to any higher power, nor do they kill for fun, torture for fun, or engage in cannabilism most of the time, as we humans do) is ridiculous. We as humans (though we've gone and squandered our gifts pretty badly) have brains that are capable of many things, and sometimes by accident of birth you're born male and feel female inside.
Honestly, it just is what it is IMHO. I don't really care whether someone wants to be called Bruce or Caitlyn, I'll call them whichever they prefer, just as if you had a nickname you preferred to go by, I'd call you by that.
The main people opposing these people happen to be (and this is fairly objective; if you look at the people stopping transgender rights it's mainly) religious folk. They object because their holy book teaches them that it is wrong- perhaps because it was written over a thousand years ago before we had the knowledge of these things, haha.