It's exceptionally perplexing because I know how I think about things is kinda atypical a lot of the time, so I don't know if this is generally how cis people think about gender or just how I personally think about gender and it's just. confusing. I really don't know.
DON'T LET SOCIAL NORMS GET YOU DOWN *shakes fist*
For many cis people, it's less of "I feel really strongly <gender>" and more of "I don't mind being <gender> and I don't really want to change so...".
cis friend: "Well, I was born with <insert-sex-here> parts, and people treated me as if I'm <gender society associates with with said parts> while I was growing up. I've never really thought about it, but I'm okay with who I am, so that's that."
other cis friend who recently learned about the difference between sex and gender: "I don't understand what you mean that gender isn't based on societal norms? If gender-differentiating societal norms don't exist, I don't think there would be any differences between people of different genders. Everyone would just not have any gender?? Anyhow, I identify with <my gender> because of my experiences, even though I don't fit with a lot of the gender stereotypes, so that's that."
other other cis friend: "well I thought about gender a lot after learning about it. I hate a lot of the societal standards put on my gender and the assumptions people make. I really don't think these assumptions fit me at all, but I decided that I like identifying as this gender, so that's that."
agender friend: "well I thought about gender a lot after learning about it... I feel really icky about all the social standards people put on my gender and the assumptions people make. I really don't think these assumptions fit me at all, and I don't really think the other gender options fit me either, so that's that."
other agender friend: "I don't know what's going on man, gender is hard."
ANYHOW my point is, gender is all over the place. Just kinda ... go with the flow, man. Don't worry about it. It's nice to have a neat label to describe yourself, but it's okay if it doesn't sort itself out.
Food for thought:
Don't think about whether you're "okay" with she/her. Would you be happier if people used different pronouns for you? If some aliens came and shoot magic beams that wiped away all societal norms, associations, assumptions, etc etc about gender and gave everyone the same-looking bits, what gender would you be?