The solution here about using the term "Birthing parent" would set a biological standard that I think most can get behind. The problem in the story in the OP isn't hung around the terms used, but on a person's want to move from one box on the page to another. If they were granted their wish it wouldn't solve the issue folks have. The problem here I think comes from the perception and use of birth certs. Some folks do not view it as a historical document and believe it should be updated to reflect a person's current situation. I don't think birth certificates should ever be amended post-fact except in cases of extreme error. Going back to your birth cert and changing your gender or name should not be a thing. But I believe this is an issue about how birth certs are used and for what reason. Birth certs should not reflect your currently chosen identity.