Definitions are important for understanding.
Woman has baby by donor sperm - defined as mother. The sperm donor has fathered a child but is not performing the role of father. If she is in a relationship with a man does he go on birth certificate? Is it defined that he is not genetic father? Should it be? What if it is donor egg and donor sperm?
Above woman in lesbian relationship, both performing the role of mother. Both on birth certificate to have equal responsibility to the child they both wanted. Presumably the birth certificate defines genetic mother? I don’t know. What if the egg was from the parent who did not carry the baby? Is that defined? And if not should it be?
Woman carries baby (donor egg) for 2 men. What is she? Both men are performing the role of father, but she’s not the genetic mother but has given birth. Both are performing the role of father. They might have chosen not to know who is the genetic father, is that defined as such on the birth certificate? Does the child have the right to know who is genetic father?
And then you consider that it’s only since dna testing became commonplace/affordable that anyone was really able to know who their genetic parents are, as you don’t actually know who gave birth to you or who provided the sperm so birth certificates were not guaranteed to be accurate anyway, obviously less likely to be fabricated for the genetic mother but the genetic father could be incorrect.
It possibly needs to be split between a certificate of genetic heritage (still not sure where a surrogate with donor egg would be defined here) and a certificate of parental responsibility. Which would possibly if it was standard for all children born fit Freddie’s desire to be named as father while still retaining the genetic information for the child for medical purposes, knowing own heritage or avoiding procreating with your sibling purposes. I’m sure there are other reasons why it is important that I’m not currently coming up with.
Being pregnant changes you, physically and emotionally. Giving birth does the same. Being an involved caregiver to a child changes you, brains change, hormone levels change whether you are genetically mother/father or not.
I think the whole birth certificate model needs updating to take into account modern fertility interventions and parental responsibility of the people bringing up the child.
Should Freddie be able with the current model to say the child has father only? No because it doesn’t fit with the surrounding law. Pregnancy should be a protected characteristic independent of gender identity. Breast feeding should be protected independently of gender identity.
If sex and gender were defined legally as two separate things this wouldn’t be necessary, but they aren’t. The law is a mess.
I hope Freddie and Freddie’s child find their way and are happy. Fundamentally, only women have eggs, only women are pregnant and only women give birth. It’s a female body process not a feminine one. Do any of those make you a mother? I’m not sure, I’m not sure what would fit. Adopted adults can visibly struggle with how to describe genetic mother versus mother/adoptive mother, the language available is emotionally fraught. I’m not sure how it could be defined without new language though. Look at the outcry on here where a step parent refers to a child mother as birth mother because birth mother is understood to mean person who relinquished the child - language matters.
Mothering makes you a mother, parenting makes you a parent. Its an active process. Transman gave birth - accurate. Man gave birth - not accurate.