Okay brass tacks time, yet again in this discussion.
Biological factors. Genital structure, chromosomes, etc. These objective facts not open for debate or discussion or "personal identity." You can not identify as a person with a penis all you want, your schlong is still there regardless of your opinion on the matter.
These is binary* and not a matter of chosen personal identity anymore than your blood type is or your eye color. These exist and are not up for debate.
*Yes edge cases of actual medical conditions causing intersexed individuals are a thing, but for 99% of the population genital structure and chromosomes and the like are a consistent binary X or Y thing.
Social factors. Society puts expectations us due to our biological factors. Men are expected to do this, Women are expected to do this. This factors are very often at best arbitrary, at worse downright discriminatory or unfair and people have every right to fight against these unwanted expectations.
These shouldn't exist. They are not actual real world objective factors, they are ones created by societies. Mens wear this, women wear this. Men act this way, women act this way. Men hold these jobs, women hold these jobs.
Which one of those is "sex" and which one is "gender" I'm so completely over caring because the more people harp on about the difference being there the less they all seem in explaining that difference. So whatever. One is sex and one is gender. Or the other one is sex and the other one is gender. Or they are both sex. Or both gender. Or one is sex is the other one is Dancing the Charleston in a Tricorner Hat While Wearing Lederhosen. I don't care.
Now the transgender discussion always seems to wind up with a lot people arguing, without ever clarifying, from the position of some third category of completely internal distinction, something that's not inherently biological like genital structure or whatever but also not socially mandated like "Only women can wear" makeup and that's when the whole thing falls apart and puts right back at the "What I'm supposed to think differently?" question which I still haven't gotten anything resembling a valid answer to.
Okay. You're a biological man that identifies as a woman. What changes? I'm still not letting this go.
You don't want a penis anymore? Well sorry... can't help you there. A good surgeon could but that takes us right back to "Well that's just admitting that something physical has to change in order for your sexual identity to change."
You want to wear dresses instead of slacks? Fine I don't care that doesn't make you a woman, it's makes you a guy who wears dresses and there's nothing wrong that but men don't have to wear slacks and women don't have to wear dresses so I can't use that as some defining factor. Again when can't have gender stereotypes which only exist when they are subverted. So again nothing changes because "Wears dress" isn't a requirement to be a woman in my head, so you wearing one doesn't make you one. In order for you wearing a dress to make you a woman, I'd have to assign "Dress wearing" to women as a defining factor and I will not do that.
And then we just wind up right back at vague pleadings about "Being considered a woman" or "identifying as a woman" which is totally meaningless which you've removed all defining factors from the term and pure passive aggressive "Oh just do what they want, it doesn't hurt anything, why does it matter?" nonsense.