There is a very good reason why no one on the trans activist side of the debate tries to explain or define any of this.
It's the same reason why the Gender Recognition Act, which refers to "male" and "female" as "genders", does not define any of those three words, despite the fact that any words in a piece of legislation which are not being used in a completely ordinary sense should be defined.
It's because as soon as you attempt to define these things, it becomes plainly apparent that the whole concept is complete nonsense.
So they choose not to define them and hope no one notices.
"Living as a woman" can only mean one of two things.
If a woman is an adult human of the female biological sex, then living as a woman means being alive, and being an adult human of the female biological sex. This means no male person can ever "live as a woman".
If a woman is a person who "identifies as a woman", then living as a woman means whatever the hell you want it to mean, because your identity is personal to you and no two people have the same one. Therefore there is no way to verify that you are living as a woman, because all it means is that you are alive and you say you "identify as a woman", whatever that means to you.
In summary, if "living as a woman" means the first of those two things, only biologically female humans can ever "live as a woman", and if it means the second of those two things, why does anyone care, what does it have to do with the rest of society, what do people who "live as women" have in common with each other, why do they need to share the same changing rooms or compete in the same sports, why are we legislating for this, what is the actual problem that needs fixing here?
But all these questions are too inconvenient so they get brushed under the carpet.
My own view is that the Gender Recognition Act should be repealed because it is completely unworkable. What does it actually achieve? Under the current law, it gives people who have obtained a piece of paper to say that they are the opposite sex to the one they actually are, following a professional diagnosis of dysphoria, the right to be treated as though they are the opposite sex (why are we treating women and men differently in the first place, if sex isn't directly relevant?) except in limited circumstances where the law recognises that biological sex actually matters.
Under the proposed new law, anyone can get this piece of paper, and the law no longer recognises that biological sex actually matters. Our sex based rights are swept aside, essentially for the benefit of people who do not have a professional diagnosis of dysphoria but nonetheless consider that they need this piece of paper with a legal fiction printed on it.
Sorry, what?
Make it make sense.