PurpleWolf, you definitely ask the right questions to make us all think!

My life experience, or what feeling like a man is not:
This is a really hard question to answer. I did not used to think of myself as a woman. I thought I was just a different kind of guy. As a child The things boys got into we're not interesting to me. The way most boys played left me trying to figure out what was even going on. I didn't really ever get to play with the girls because that was cause for being made fun of. That I learned very quickly. I avoided things girls did and avoided the girls themselves. I was felt drawn to them and so being around the girls was off limits as was anything seen as girly. So with the boys I was always feeling left out and three steps behind trying to figure out "how" to play the way they did. I managed to fudge my way through and act just male enough to not get made fun of generally. I never did feel like I fit in.
Looking back, being a kid was hard. I never developed good social skills. Being around other kids took effort. I was constantly observing the boys and awkwardly tried to figure out how to be like them. Seems like my entire social life in school was just trying to be as invisible as possible.
Then there was the emotions. Boys are mean to each other. It's the way they interact. I never could understand that. I tried a few times to emulate it but always ended up feeling awful for saying something mean to another. Oh EMOTIONS, yeh boys don't allow that. Funny thing was I always thought that the other boys all had to fight every day to not show them, to not cry when another boy was a jerk to you. I had to learn how to compartmentalize my emotions. I actually did fairly well at this over the years but I also avoided almost everyone after high school that I could. I focused my mind on logical things. I ended up working as a mechanic for a long time. Machines are logical. They require little social interactions and keep the mind occupied.
Men still make little sense to me. As an adult I worked traveling to business locations to work on large machinery. The guys working in these places often tried to get me into their rec time conversations. These invariably went to gross talk of objectifying and using women sexually. Sometimes cars and other "guy" stuff. I kept my mouth shut when they would talk about women. Somehow I always felt offended by group guy talk like that. I never felt like guy talk was particularly interesting to me.
My more feminine experience:
I have always felt more of an association to the girls even though I avoided being around them for so much of my formative years. As an adult, when I was allowed into a group of women talking, I find the conversation, I suppose "relevant" is the best word. It is interesting and actually enjoyable to be part of. Like I actually just feel good in general after being in female conversation. Everything is just sort of more natural. Like I actually do understand why the conversation goes as it does. I understand more what other women are thinking and feeling. It's really the opposite of being around a group of guys talking.
OK so living as a man, everyday was a limited life. I had to monitor how I acted, how I walked even. I trained myself to walk toe out more back in Jr. High to be like the other boys. Sometimes when explaining things to customers at work I had to mind how I used my hands when talking. I don't know why that was. There were occasions whe a guy would start looking at me funny because of how I would talk with my hands. I would pick up on that and immediately put my hands into my jean pockets. I think that the issue was, emulating guys was a conscious effort while acting as I had seen females act over my life was more natural. Being in the MidWest US a guy talking with his hands like women actively do is a big no-no. Basically expression of emotion while speaking is another.
Living as a man was just plain unnatural for me.
Living as a woman is FREEDOM. That is the best description. I do what is just natural for me. I do not have to suppress my emotions. I don't have to consciously think around the emotional part of my mind. The best description is that my feelings are now "free flowing". Like feeling is completely integrated in my thoughts. I just plain don't have to fight my own mind anymore. I get to talk about things that are important feeling to me. I can express my true inner instincts without fear of ridicule.
The problem with these type of questions is that someone like myself, who is very binary female, can't really answer what not feeling like a woman is. I can only describe what not feeling like a man is.