thats a fairly common cis thing tbh. some say its one of the biggest definitions of being cis.

for me, a binary trans woman, i felt very off during puberty. it just didnt feel right. i got suicidal as hell and i couldnt really grok that the reason why was because i was trans. i knew before puberty that id rather be a girl but that was a very abstract concept that didnt matter much to me at the time, kids honestly didnt look that different. but when puberty hit, i hated everything happening to my body. none of it felt right. looking more and more like a guy disgusted me and all the adults in sex ed were just saying things like 'its normal to be weirded out by puberty or feel uncomfortable with it' and i internalized that maybe what i was feeling was normal and typical of guys. like of course, all guys hate getting hairier and more muscular and stuff! so i kept with the puberty for a while and all it did was push me further and further into depression until i snapped, attempted suicide, and got on hrt shortly after when i became an adult.

i think there is definitely some sort of chemical component to hrt and being (binary) trans, even when i was just 3 months on hrt i felt immensely better despite only looking a bit different.

anyways, back to your question: well, i dont really know what its like to 'feel' like a woman. that feels very abstract to me. i just know i love estrogen and how it makes me feel and how it affects my body and mood. i feel weird looking in a mirror and seeing masculine things that arent typical on women, because i know that my first puberty fucked that up. idk, its a bit like being a cis woman that grew a beard or something. its normal in our society to get that sort of thing treated. and no one second guesses that it is disconcerting.

i sometimes would think to myself before transition 'would i get on hrt if i had been on an island by myself and never knew what a man or woman was?' and i had such a hard time answering that question. now, id definitely say yes, even if i had never known about women or men, the mental effects of estrogen are just better suited for me.

for me, the reasoning behind wanting to be treated like a woman and being named like a woman is relatively simple. i look like one now and its just far easier to deal with. i dont like being referred to as a man because that implies someone sees something masculine about me, which is a personal pet peeve of mine, i feel like its like pointing at a woman and saying 'look, she has a beard!' its just rude.