President of the High Court Family Division, Andrew McFarlane, ruled against McConnell's request to be registered as the father.
"There is a material difference between a person's gender and their status as a parent," the judge said.
"Being a 'mother', whilst hitherto always associated with being female, is the status afforded to a person who undergoes the physical and biological process of carrying a pregnancy and giving birth."
"It is now medically and legally possible for an individual, whose gender is recognised in law as male, to become pregnant and give birth to their child."
"Whilst that person's gender is 'male', their parental status, which derives from their biological role in giving birth, is that of 'mother'."
The new father told The Guardian: "If it is upholding the status quo then I am really worried about what this means not just for me but other trans people who are parents or who want to become parents."
"It has serious implications for non-traditional family structures. It upholds the view that only the most traditional forms of family are properly recognised or treated equally. It's just not fair."
McConnell started testosterone treatments in 2013 although he retained his female reproductive system.
In 2016 he paused the hormone treatment so he could get pregnant from a sperm donor..