Q1: A lot of this question seems to be more about the definition of "binary", so it's just word games? Some, like Jane Clare Jones, say that sex is NOT a binary because she interprets binary to mean "X or not X". She would say there are exactly two sexes, but having "two" of something does not make a binary.

There are exactly 2 sexes because there are exactly 2 roles in reproduction (for the creatures that it applies to). You need exactly 1 of each gamete to make a new creature. 2 gametes, 1 of each sex = 1 child.

Which of the 2 reproductive roles an individual may play, and how that is determined, varies somewhat more. When we say a creature is "male" we mean it is organised to produce the male gametes. A creature that could produce both would be a hermaphrodite - not something ever observed in humans. If a creature changed from producing one to the other, it would be a sequential hermaphrodite. Again, not something humans do.

So you say "Why don't hermaphrodites show that in other sexually reproducing species sex is not a binary?". That's a question about the word "binary". There are two sexes. An organism of a 2-sexed species can be one, or the other, or both, or neither, in principle. But humans have never been observed to be both, and there is no "unsexed" development path for humans, only infertile humans that failed to go all the way down the male or female development path.

There are certain common DSDs that occur - some are sex-specific, and others present differently in males and females - but they're not a new sex, any more than Downs Syndrome is a sex. A condition that causes infertility is not a sex.

Q2: We're talking about the type of organism they are. A cat isn't less of a cat if you chop its legs off. An elephant isn't less of an elephant if you remove its tusks. A peacock isn't less of a peacock if you remove its feathers. Our technology is almost purely cosmetic - it's mostly surgery with crude use of hormones to stimulate development of secondary sexual characteristics. You're making a male more feminine or a female more masculine. You're doing absolutely nothing to their actual sex. And male/female are sexes. Not sex characteristics.

I remember being young and reading about "sex change surgery" in the 80s, I guess. I was rather flummoxed at the time - it seemed out of line with what I knew about medical technology. Surely we weren't able to do that? If we did, how on earth did it work? I felt rather cheated when I found out what they meant - hormones and cosmetic surgery, no actual sex change. Bunch of liars.

If we were to make a similar argument about other classifications, it would be: Backbone (the feature) = mammal (the category). Any number of vertebrates could have backbones

Eh? backbone (the feature) = vertebrate (the category).

verterbrates with mammary glands (the feature) = mammals (the category).

(The clue is in the name in both cases!)

What you said only didn't work because you mismatched the feature and category.

Males produce sperm, because that's the definition of the word male - the sex with the small mobile gametes.

So then it seems "those that produce eggs are women" or "those that produce sperm are men" is incorrect, as one does not need to have/produce eggs to be a woman or have/produce sperm to be a man.

Ah, the good old "a broken clock isn't a clock" argument. It is possible to be an infertile man, or an infertile woman. We have words like "broken" and "infertile" because we know that something in a category may fail to fully perform its function.

If you deny that, you deny the meaning of the words "broken" or "infertile".

But, given an infertile person, you can readily determine what sex they are, and whether you should try to treat them to make sperm or eggs.

I would hope a transactivist presented with an infertile person wouldn't try to pretend they didn't know whether they should be trying to stimulate sperm production or ovulation.

Really, all this stuff is just sophomoric philosophical flimflam that works equally well with any sort of categories. But the notable thing is that this desperate pseudo-intellectual energy is only applied to sex - specifically females - because male humans desperately want to LARP as women and get into their spaces.

It's almost comical how desperate they are. I'd be embarrassed to come up with this tosh.