No our sex does not define our gender at all. Sex and gender and two separate things, that society has tied together.

Society tells us that if you have a vulva, you should 'naturally' be interested in cooking and dolls. And that if you are born with a penis, you are 'naturally' more aggressive and most likely love cars and bikes.

But these are ideas that we are given very early on and then we internalize them.

So no, our sex does 
not define our gender. Good cooking skills or excellent physical stamina is just a reflection of our individual interests and abilities.