There is a process to amend birth certificates, presumably initially intended for errors like this. But then people who successfully transitioned used the process to amend their birth certificates to reflect their new gender, because there was no other way to do it. The transphobes seized on this, and started processes that refuse to honor any late changes to birth certificates.

It should have been a simple matter to resolve - his doctor wites a note saying "This kid has boy parts, and always has. The birth certificate was always an administrative error". But then, that would force the transphobes to acknowledge a role for facts and science to contradict their feelings. So, we can't have that either.

So, they go on claiming that they are just out for the best interests of kids, and that justifies why they are treating this kid so poorly. When in reality, they are just protecting their narrative, at his expense.