I can maybe clear that first one up for you a little. Otherwise, I agree. The language is changing at a breakneck pace and people need to get some thicker skin and learn some patience.
Females have periods. All mammalian females have periods or cycles.
Being female is your biological sex. You have a XX chromosomes. Your reproductive organs are two ovaries and a uterus and other structural tissues/organs. Upon reaching puberty, you will grow breasts that will produce milk to feed your offspring if and when you have some. Note that having periods is only relevant to part of the life cycle of a female; but males never have periods.
That's it.
Being a woman is a gender. It's as much or more part of a socialized expression of being as it has anything to do with your sex. While most females are also women, that's not a given. Being a woman has to do with one's place and allowed roles in society, how they dress, how they behave, how they're raised, etc. It's an organizational feature amongst humans. It's a particular expression of self.
So. from here we can see that females have periods during part of their life cycle.
Men sometimes have periods too but males do not.
Nonbinary person's may potentially menstruate as well which may be a function of their gender or their sex as some of these folks have more or less than the usual 2 chromosome pair that determines sex.
Basically what this person was saying is that not reproductively female people are women. Some of them are men because they align with the masculine expression of self.