Lawyers representing the parent told a judge that he had been biologically able to get pregnant and give birth but had legally become a man when the child was born.
The man wants to be identified as the child's "father" or "parent" on a birth certificate, however a birth registrar told the man the law requires people who give birth to children to be registered as mothers.
The man has since taken legal action against the body set up to administer statutory provisions relating to the registration of births and deaths after complaining of discrimination.
He said forcing him to register as the child's "mother" breached his human right to respect for private and family life.
The man added that such "interference" was not proportionate or necessary in the light of changes which had "evolved in society".
Mr Justice Francis yesterday heard preliminary arguments from lawyers representing the man and lawyers representing The Registrar General for England and Wales at a High Court hearing in London.
The judge said the issue had never been raised in a court in England and Wales before. He added that if the man won his fight ministers might have to consider changing the law.
Mr Justice Francis heard how the man was born a woman but "realised he was trans" several years ago.
Lawyers said he had lived "as a man" since then and had undergone surgery to "re-contour" his upper body.
The High Court judge was told that the man was granted a gender recognition certificate more than a year ago, before the baby was born.
In brief | Transgender issues"It is an accepted fact that a female who transitions to male may in law maintain the ability to conceive and give birth to a child," barrister Hannah Markham QC, who leads the man's legal team, explained in a written outline of his claim.
Transgender
'Transgender' is the umbrella term for people who identify with a different gender from the one they were assigned at birth - often diagnosed as 'gender dysphoria'. The term 'transsexual' refers more specifically to someone who has had medical intervention, and is considered archaic.
Public awareness
The number of people being diagnosed with gender dysphoria is on the rise, as public awareness increases. When Caitlyn Jenner appeared on the July 2015 cover of Vanity Fair - her first photo shoot since coming out as a trans woman - Google searches of the word 'transgender' reached an all-time high worldwide.
Surgery and hormones
In the UK and most countries around the world, children need to wait until they are adults before they can undergo gender reassignment surgery, but they can be prescribed synthetic hormones to suppress puberty. The NHS says the effects are fully reversible, so treatment can be stopped at any time.
Age limits
There is no specific age when puberty-suppressing drugs can be prescribed: it depends when a child goes through puberty. The US state of Oregon recently made it legal for 15-year-olds to undergo gender reassignment surgery; most countries that do allow such surgery (including the UK) require the patient to be 18 or older.
Military service
Under President Obama, legislation was introduced to allow transgender soldiers to openly serve in the military. His successor, Donald Trump has announced plans to rescind that policy. All branches of Britain's armed forces welcome transgender recruits.
"(He) seeks a declaration that being forced to register as a mother to his son is contrary to his right to private and family life within Article 8 of the Human Rights Act 1998 and that such interference, in the light of the changes which have evolved in society are no longer proportionate...
"Further (he seeks) a declaration that the current forms utilised by the Registrar General to record parent and parent identity discriminate against trans and intersex parents."
She added: "It is further averred that the current law relating to the registration of births and deaths is no longer compatible with the changes in society, the evolvement of freedom of expression and gender equality and the protection of an individual's rights to identify as a particular gender."
Barrister Sarah Hannett, who is leading the Registrar General's legal team, said the man had obtained a gender recognition certificate under the 2004 Gender Recognition Act.
He gave birth following intrauterine insemination treatment some months ago.
She said the Registrar General took the view that registrars were not permitted to "take the step in question".
Comment: Babies are only born of women.