Sex (your biological characteristics, your chromosomes/DNA, ability to produce gametes of one type or another, etc) is binary *in humans* and cannot be changed. Even intersex people, who justifiably have complex experiences with sex, can be categorized as either having an intersex condition arising from an anomaly on the female pathway or the male pathway. Scientifically, we know this. It is a post-modern fallacy to suggest that sex is undefinable or a useless framework just because human genetic variation is so broad and complex. (Y'know what else is broad and complex? Life! We don't fully understand it, but no one is earnestly trying to say that life doesn't exist!)
Gender is the superstructure which is built upon sex. It is socially constructed. Gender is what says that you will be a housewife because you are born with a vulva, or that you will have the right to vote because you are born with a penis. Gender both invented and enforces our ideas of femininity and masculinity. Gender, currently, is used as a tool to reinforce systems of patriarchy and misogyny. Did you think it was a coincidence that "femininity" is associated with rituals to constrict movement and diminish power, whereas "masculinity" is associated with rituals to expand movement and bolster power? (e.g. femininity is associated with clothes that restrict movement, with beauty rituals that systematically steal time/money/energy from women, with hobbies that focus on serving others instead of self-improvement, with constant self-objectification/ sexualization and giving pleasure instead of receiving it, with expectations to do unpaid labor as a mother or housewife. masculinity is associated with clothes that give freedom of movement, with beauty rituals that cost significantly less time/money/energy, with hobbies that focus on building skills, with sexual dominance and gaining pleasure instead of giving it, with expectations to do paid labor and serve in positions of authority in the community.) Do you think this system sprang up in a vacuum? Do you not see how this system of gender is a system that upholds men in power and women in subservience?
(Note: Gender need not be wielded in this way. Gender norms can be changed to be beneficial instead of harmful. But that is a whole other discussion in the realm of speculative feminism.)
Looked at this way, we do not say that "amab trans people are dangerous perverts." We say that amab people, people born and raised as men in a society that caters to men, will be raised with a certain way of thinking and behaving. This leads to astonishing statistics in which men ("amab people") commit 99% of the rapes and in which women ("afab people") comprise 91% of the victims. And more! Take in the stats below and try to tell me that there isn't a clear pattern there.
Trans people, despite what you want to believe, statistically do not break this mold:
"MtF transitioners were over 6 times more likely to be convicted of an offence than female
comparators and 18 times more likely to be convicted of a violent offence. The group had
no statistically significant differences from other natal males, for convictions in general or
for violent offending."
If you just look, you'll see that trans women by and large behave just the same as men, and trans men by and large behave just the same as women. If you do not acknowledge this, you are left with questions like, "why do trans women go to prison for rape and sexual assault at a much higher rate than cis women or even cis men?" (source below from the same parliament document above). Or: "Why are trans men comparatively so rarely convicted of violent crime that it hardly shows up on a Google search? (If they were really the same as men, why wouldn't they behave the same?)" These are just examples. My anecdotal experience also suggests that trans men / afab trans people are also likely to have eating disorders and other pathologies at rates similar to sexual minority cis women. They are also likely to experience sexual assault and other forms of misogynistic oppression at the same rates as cis women. (I acknowledge that the research has not been done on this that I can find, so feel free to give this point less weight. However, I have been deeply involved in trans community for many years now, and the number of afab non-binary or trans men I know with eating disorders, depression, or OCD nearly equals the number of lesbian/bisexual women I know with eating disorders, depression, or OCD. Just as an illustration.)
Given all this, a system of gender emerges in which individuals are raised in a system with extremely strong messaging about "men" vs "women." Being female and gender non-conforming or a lesbian or anything that doesn't fit the mold will inevitably be extremely distressing. If the messaging is thus that "if you don't feel like a women, then you aren't one!", of course many women who are bothered by the fact that they don't fit the mold will latch onto that reasoning. (I know I did! You can look at stories from other detrans people to confirm this as well.) Men are more complicated. They either tend to be drawn towards "womanhood" because they similarly do not fit the mold of "man" and they crave a sense of belonging, which I'm sympathetic towards. In other cases, men are creeps who fantasize about being women as a way to exert sexual control over women. Look at the #terfbreaking or #transfem superiority tags as an example of this depravity, or read stories from detrans men who recognize that they only identified as women as a response to their autogynophilia. The pattern exists, even trans women admit this pattern exists. It will continue to exist whether you accept it or not.
Radfems, in general, support gender non-conformity!! Conservatives will whine about women with hairy legs and men in dresses as if those are problems themselves. They're not. I hope every man who wants to be in a dress (for non-pervy reasons) can wear one without judgement or shame. I hope all women feel empowered to give up shaving or take up weightlifting without judgement or shame. I support people changing their names to something that feels more correct. These are good, these break down gender norms and lessen Gender's power over society. But the minute you start to say "well, I must not be a woman because I do X activity" - that reifies Gender! That keeps it alive! That's conservative values with a progressive veneer! Don't you see??
Now let me get one more thing clear. Radfems do not believe that women are automatically weaker than men. Women *tend to be* physically weaker due to their *tendency* to be physically smaller and men's *tendency* to build muscle faster. Women also tend to be weaker due to a lifetime of conditioning that women must be small and weak and skinny, that women shouldn't work out lest they get too bulky, that women shouldn't eat that much lest they get fat. These messages are weapons against women that keep them vulnerable to men.
I'm gonna make this huge:
Women do not, under any circumstances, need extra protection from men. No radfem will ever or has ever said this. Women need to protect themselves and stand with each other.
Finally, sex separation (not segregation. It's only segregation when the oppressor is enforcing it) is not the only means of protecting women, but in a world that says that women need men to do anything at all, female-only spaces say "we don't need men to thrive or even survive, watch us do it all ourselves!" which is a powerful, radical message that pisses off a lot of people (including you, apparently). Separation shows that if women want, we could disconnect from society so radically that men would be bereft. The patriarchy needs women to be subservient, to do labor and to make new people who will continue doing labor. Separatist women say "fuck no, we're opting out."
Okay... I think that covers it.
I'm not expecting you to change your mind, btw. Just laying out the facts of what we actually believe and why we believe it.
Remember, this is just the radfem perspective on gender and trans issues, specifically, with some of my personal views sprinkled in. (Since this is the piss on the poor website: my personal views are denoted with "I/me/my" sentences, in case you need help differentiating them). There is so much more to be said on other issues, on our core theory, on our ideas to build a better future. That is all outside the scope of this post.
Of course, let me know if you have any questions, would like to see more sources, or would like me to point you in resources to do your own investigating. You can hold whatever position you like in my book as long as you're actually informed. :)