This is how we'd instinctively teach a small child pronouns.
"You can't see the bin? OK. See the woman over there - she's wearing a blue coat? Well next to her there's a man with his dog. Yeah? He's sitting by a person with their back turned. Well next to them is the bin. Off you go!"
We all internalise this stuff.
Woman, girl, female =she, her
Man, boy, male=he, him
Not sure, generic, mixed = they, them
Most people believe, and currently this is the UK law position, that a woman is a human female of any age ie including girls and a man is a human male of any age ie including boys. So in UK law, Woman and Man are the names of the Sex classes.
Approximately 5000+ people in the UK have got a Gender Recognition Certificate which gives them a new birth certificate with a change to the original sex marker as observed at birth. They have swapped legal Sex classes. Holders of a GRC still remain biologically male or female so, in recognition of that fact, there are exemptions in both the GRA and Equality Act 2010 with regard to Single sex spaces, inheritance etc.
Some people, on the other hand, believe that only the words 'female' and 'male' are sex terms and that the words 'woman' and 'man' are purely gender terms. **
This means they believe that a woman can have a penis or a vagina, have cervical or prostate cancer, be male or female. Ditto for men.
These people believe Gender - how you feel about yourself and identify - is more important than biological Sex.
In this world view, you get to choose your own pronouns and they don't have to 'agree' with either your biological sex or even how you present - your gender expression.
One consequence of this is that the internalised system we all learned as small children of 'assigning' pronouns based on sex class (and which we generally manage to do with almost 100% accuracy by the time we are adults) is being linguistically dismantled.
Yet we still retain all the myriad instinctive ways we have accumulated over the years to decide what pronouns we assign to an unknown person (some of which are biological sex based: gait, build, face shape, pelvis shape, Adam's apple, hair pattern, voice etc, and some of which are more gendered: name, clothing, socialisation etc).
There is, therefore, very real cognitive dissonance when we are asked to use gender based pronouns untethered from biology, when our model since childhood has been sex based pronouns. Hence the move to get everyone to share their pronouns as if they were all up for grabs. Did cat girl really need to tell us she was she/her?
Unfortunately, the unstable sense of self at the heart of so much of the gender identity movement - though entirely developmentally normal in young people - is made even more vulnerable by handing over identity control (via the means of pronouns) to external people. Your identity is only 'valid' as long as no one misgenders you. Hence misgendering being 'literal violence' as it is an assault on your very sense of self.
**We are also seeing evidence of a more extreme belief that even 'male' and 'female' are also gender not sex terms. In the WESC yesterday there was reference to trans female - meaning?
kareningalasmith.com/2021/04/21/counting-dead-trans-people/
All of which leaves the adult human female kind of woman in a terrible position because we have had the language to describe our legal status and sex class co-opted without consultation or consent.