Gender is defined as: the state of being male or female (typically used with reference to social and cultural differences rather than biological ones).
For most people, your gender and your sex are congruent. For others, it isn't.
The definition of gender is not universally agreed upon. And it's pretty obvious that that definition is not the one the person you are replying to uses.
Definitions are also not fact, by definition.
There are plenty of valid arguments for calling trans people the gender they want to be. This isn't one since it isn't going to convince anyone who doesn't already agree with you.
Edit: The why do you care part is a valid argument, was addressing the rest of your comment
Gender is defined as: the state of being male or female (typically used with reference to social and cultural differences rather than biological ones).
For most people, your gender and your sex are congruent. For others, it isn't.
Even if you don't agree: Why do you care?