Some thoughts

I don't understand gender, either. I'm a woman because my body is female, and that's it. I don't know what it means to "feel like a woman", so I don't even know if my gender is female, but I don't care. I sometimes feel more like what is considered "female" and sometimes more what is considered "male", but since these are all just stereotypes and roles I don't really consider it feeling male/female.
I had some problems with having a female body in the past, but I don't know why. Maybe I was because of all the stereotypes that society made me think I had to meet.

 

I dunno. I look at 99% of normal, basic, semi-attractive men and think, I want to look, behave, and be treated like them. I want to have pecs and shave and wear classic men's clothes and shoes cologne and revel in my culture's idea of masculinity and paint my very walls with it. I love it, therefore I want to be it.

 

It's complicated. In the end, whatever gender might mean, and whatever might cause people to identify with a particular gender, transgenderism exists. For some, it causes extreme discomfort and body dysphoria, and for others it doesn't. I don't know the answers. I can explain how I feel about my own gender, but I can't speak for anyone else's experiences or tell them how to feel.

But no matter what, stereotypes and social expectations are frustrating, and the sooner society moves on from those, the better.

 

I had all the questions you had, so I'm gonna tell you the conclusions I came to. A lot of people might disagree. This is just my perspective.

I think most of gender is bullshit. We all know gender roles and stereotypes are dumb, and we always say they don't define gender, but I can't begin to image what it would mean to "feel" like a certain gender without the context of these predefined roles and stereotypes. I wholeheartedly believe that the "feeling" of gender would not exist if we did not have these arbitrary descriptions of what it means to be socially female/feminine and male/masculine. The only thing that would be left is people who have physical dysphoria (probably caused by their brain map not lining up to body parts they actually have, although more research needs to be done to confirm that hypothesis), which is why dysphoria makes the most sense to me as a definition of gender. I am a man because society decided that the people with penises, deep voices, facial hair, etc. are called "men", and I am uncomfortable without having most (if not all) of those characteristics. It has nothing to do with whether I'm tough or considerate or action-oriented or emotional, because you're right: both men and women can be all of those things. And I have no idea what it means to "feel" like a gender because I don't think there's any one thing that all men feel (and most cis people describe not really feeling their gender, which suggests that it's only something you really "feel" when you're uncomfortable with it). Honestly I think the idea that everyone has some inherent feeling of gender doesn't really make sense. The words "male" and "female" were created to describe the what you've got in your pants (and then gender roles and stereotypes were built around that), not to describe some feeling deep down that everyone had but didn't know what to call it.

I'm going to transition because my brain doesn't think I have breasts so it's uncomfortable and alarming to look down and see them, or to be able to feel that they're there. If I take testosterone, it'll be to cope with the days where I look in the mirror and don't understand why my face looks like I haven't gone through puberty yet when I'm 19 (because my brain expects me to go through male puberty) or I open my mouth to talk and it's way higher than I expect it to be. The social parts of transition emerge from the physical dysphoria; I want to be called by a name that most people think of as male and by he/him pronouns because being called "she" just reminds me of the parts I have that make me uncomfortable. Even if I got top and bottom surgery and went on T, it would still feel really weird to be someone who had all the physical signs that fit the description of male and to still be called by a name and pronouns that people associate with women.

 

OK here's my take on it all, for what it's worth.
What we know for sure is that physically speaking, a person's sex is determined by genes and hormones fall on a spectrum that ranges from "manly men" to "girly girls" with most people falling somewhere in between. Because we all start as female and require androgens to masculinize us, there is really only one double/ "M" bell curve that covers everyone, with people with xy chromosome on o e side and xx on the other side. Now, for the purpose of reproduction nearly everyone fits in the binary categories of male or female with a very small percentage of people being intersex, they are the center of the bell curve, the middle low point of the M and often having a chromosomal anomaly. But further out from the middle you have trans people, with Ftm and mtf folks close to center and having brain structures closer to the opposite sex due to hormonal anomalies during gestation. Then further towards the outside you have cis people. But that's all about the physical aspect, not just sex but brain structures, physical reasons for trans people existing.

Gender, however, is a social construct. It's related to genetics, look up epigenetics/genetic memory. Gender is the social role that your physical state predisposes you to. In older societies there seems to have typically been 3 or more genders, so people who were trans had a social role that was respectable where they could function in the community as they felt inclined to and express themselves freely. Eunuchs, 2-spirit people, Thia "ladyboys", are all examples of non binary gender roles that are accepted parts of their respective societies. It wasn't until after Christianity was adopted by the roman's as the state religion and other beliefs became persecuted that trans people where singled out and a binary gender system was enforced.

Once the binary system was enforced, trans people had very few options for functioning in society. With no natural role for them to fill they would probably have done the same thing many of us still do, spend half their life trying to be one gender and then transition, if they could. It was probably easier when all you had to show was your face behind a veil, but we lost the ability to be open about who we are.... and here we are today, fighting to get it back, and evolving new ways of expressing our identity through medical intervention. It's really an amazing time to be a trans person, we are literally defining the field for the first generation of people in modern western culture who will not know what ots like to grow up ignorant of everything outside the gender binary.