Wow, I think this whole thread sums it up well, but I really related to Sephirah and Mogu's descriptions of it.
Personally, you don't even have to see it as male/female. Just imagine it as two different sets of behaviour. It's as if EVERYTHING that just comes natural to you, your natural actions, behaviours, feelings, the words you use/want to use, the expressions you make, how you carry yourself et cetera, fits into one behaviour set, whilst everyone is constantly forcing you to live as if you should be using the other behaviour set simply because you look more like them. So you have to live with the constant frustration of curbing your behaviour to fit the set that's expected, whilst constantly feeling anxious that you're not doing a good enough job at it.
From very young, I was made aware that how I did things was wrong (too emotional, too expressive, too submissive, too introverted, too extreme, too musical, too artsy, too feminine in every way ugh) and how the boys did things 'right', but whereas they didn't have to work at it, I spent every day (until my dysphoria anxiety attack kicked in that led to me coming out to myself) working to try and fit in, which often led me to overcompensating and becoming overtly masculine (you want me to be a male, I'll be a freaking male).
Meanwhile, you see people that behave and act and think and talk the way you naturally WOULD and everybody just accepts them acting the way they do 100% without question. It's horrible, it's like constantly feeling like a second rate citizen, you work to fit into your traditional gender role (whilst never really succeeding, even if you pass socially, it always feels fake for me) whilst you're surrounded by people that share traits just like your natural traits yet YOU can't be that way because... well I don't even know... because it breaks the traditional idea of gender roles?
I'm still trying to work out exactly the extent of the feeling, and this might be just how I see it, but yeh...