it doesn't deny them the knowledge, that's the point. Most people who put "mother," trans men could put "birth parent", and it provides exactly the same information. There is no trauma, no lack of information, no removal from history and no problem.
You're really not getting this, are you DadJoke? It matters not one jot what a woman who doesn't want to be a woman wants to be called for the purposes of her child's birth certificate. Because it is not her certificate. It does not document her birth. It documents her child's birth. Every single child on this planet has a mother who gave birth to that child. Every child has a right to know who that mother is. It's completely irrelevant whether that woman would rather not document her child's birth than be registered as the mother of her child. Because it isn't about her. It's only about that child. And the child has rights that exist independently of its mother. Said rights include the right to an identity, part of which is knowing which woman gave birth to you and is therefore your birth mother.
I know the fact that other people have rights, too, is a difficult concept for many proponents of the doctrine of gender identity, but we would make a lot more progress in this debate if that knowledge would register. And in this case, the right lies solely with the child.
This is not about the birth mother. This is not about what she wants to be called. This is about the child, who is entitled to an entry under the field "mother".
It's also rather disingenuous to be arguing about "birth parent" when the whole case is about a female person who wants to be registered as the father, thereby denying the child its rights to knowing its own mother.
And it's pointless to argue that these particular children will know because of all the publicity. There's no doubt about it - look at law proposals in other countries if you need proof and the ideas brought up here by trans rights organisations - as soon as a court allows the mother to be registered as the father, there will be children denied the knowledge of who gave birth to them, and it will be denied permanently by those women and men who will not countenance any reference to their birth sex.
We have some protection in the UK for donor-conceived children, who now have a legal right to know who their biological father (in cases of sperm donation via a clinic) or mother (in cases of egg donation via a clinic) is. And it took a very long time for children to be given even that much, but anyone who donated sperm or eggs after 1 April 2005 had to accept that the UK Parliament decided that donor information also belongs to the child conceived using the donor's sperm or egg.
It took 60 years to get to this point and the first children allowed to know the name of their biological father or mother under this law will not be able to ask for that information until after 1 April 2023 at the earliest.
In the meantime we have had decades or research into donor-conceived children who had no way of ever finding out who their biological father was (and latterly biological mother) , and the psychological issues this caused them. That's because humans have an inherent need to know where they come from, and as we now know, babies do have an inherent need to be with their birth mother (the discussion around this need has led to the phrase the "fourth trimester" being coined).
This is why in cases where a parent transitions, UK Parliament decided to provide protection for their children through the Gender Recognition Act. This sets out that children of parents who have legally changed sex do not change their legal relationship with that parent - the father remains the father, even if that father is legally a woman and the mother remains the mother, even if that mother is legally a man. This was done specifically to protect children.
If a court changes that legal rule, it will create a situation where children will be denied vital information about their own history. And we already know that this damages the child's wellbeing.