Great question deadman
To answer your question, dead, it is rather complex. The notion of not feeling like a man or a woman, at its core stems from gender dysphoria. Take me for example, because I hated my male body, it made me a lot more aware that I didn't feel like a man. Since most people don't suffer from gender dysphoria, they probably don't think of their sexual identity as a big deal, because they are ok with their body.
I am aware of the actual conditions (gender dysphoria and GID) involved and the technical definitions. The problem is that those are very clinical. They are a set of symptoms coupled with vague reasoning as to why. It doesn't help me to understand.
Specifically the bolded part is what confuses me. To my way of thinking - which admittedly is only vaguely close to what most people would consider sane on the best of days - this is the same as waking up and hating the fact that you have arms. I do understand hating aspects of your body as I have a rather rare genetic condition that contributed to my crippling but I can't quite wrap my head around hating your sexual identity.
In my development I have never undergone sexual confusion or a sense of gender dysphoria. I had other issues. Mostly anger related. So this line of thought is just alien to me and I'm trying hard to fully understand. Hopefully I am doing so in a respectful manner. I'll be honest. Tact is not my strong suit.
That is not dead which can eternal lie and withs strange aeons even death may die.