A true father is a social contributor, not a biological one.

“Nooooo”, our two-year-old daughter corrects me in her customary sing-song voice, “not two mummies!” That takes me by surprise.

I am her mother and so is Deb, my partner of 12 years. When we were lucky enough to have a baby, it never occurred to me my daughter wouldn’t think of us as her two mummies. We tried for over six years to get pregnant, so I had plenty of time to buy into the romance of the two-mummy family.

I’d heard straight friends mention this or that kid in their own child’s class with two mothers; and as soon as we started trying to conceive, I’d trawled Amazon for children’s books depicting kids with same-sex parents, like that American classic, Heather has Two Mommies. Of course, the root of my daughter’s disavowal was no more than the simple fact that in our family I’m known as Mummy and Deb is known as Ma, names we assigned before she was born.

We hadn’t opted for symmetrical titles like lesbian mothers Bette and Tina did in the American TV series, The L Word, who called themselves “Mama B” and “Mama T”. So, as far as our daughter was concerned, it’s preposterous to suggest she has two mummies: clearly, she had one Mummy and one Ma.

It’s such a common-sense proposition, yet when I delved into it I found myself running headlong into several assumptions about us as lesbian parents. I realised I had assimilated the lesbian parenting model constructed for us by the outside world. It’s society that constructs us as a female parent conglomerate, not our daughter. She discerns us in the specific, not the generic. Ma takes her to the park to feed the ducks and Mummy makes her laugh by putting a nappy on her toy chicken.

When we signed up for donor insemination at a Sydney fertility clinic, we were reminded that some segments of society would always regard our family as incomplete. Before starting treatment, we were required to attend a counselling session.

We turned up hoping to appear as worthy and well-adjusted as possible. Smiling benignly as she jotted notes onto a pad, the psychologist trod a path between friendliness and professional aloofness. She nodded sagely as we spoke on a range of issues which I can no longer recall now.

What sticks with me, however, is something she told us; something she said was crucial for us to accept should we conceive a child with donor sperm. We inched forward in our seats. We needed to understand was our child would always have a father. We sank back in our seats.

By that logic, we were already incomplete as parents—even before we’d had a child. Then we bristled with indignity. This medical professional was telling us that the guy who ejaculated into a cup in the treatment room next door (for $25 plus travel costs) would have equal status to us—the two people who would rock our child to sleep, wipe her nose and beg her not to bring snails inside the house—in other words, the people who would be there.

They had a name for such people: the parents. I knew instinctively there was something wrong with the assumptions behind the term father as the psychologist was using it. This hypothetical male donor whose contribution—don’t get me wrong—we were immensely grateful for, was just that: a contributor of genetic material, not a father.

I felt slighted for us, but mostly I felt slighted for our own fathers who had been, and still are, loving and present parents—Deb’s, who taught her how to ride a bike; and, mine, who brought me jelly-babies when I was home sick. The word father carries semantic weight in excess of a mere sperm donor, I told the psychologist (who no doubt scribbled on her notepad “radical lesbian feminazis”).

A true father is a social contributor, not a biological one. Being adopted myself, I have direct experience of this: my real parents are those who guided me through my life, not those who conceived me. And, like my parents had done with me, when the time is right we will tell our daughter in age-appropriate terms about this special person who helped us become her Ma and Mummy.

It was when I turned the psychologist’s question around on itself that I realised the scope of her prejudicial attitude: Did she tell heterosexual couples who sought donor sperm to conceive that their baby would always have a(nother) father? No, I didn’t think so.

With a heterosexual couple, the social placeholders of Mum and Dad are already filled regardless of the biological truth of the child’s conception: there is no glaring male absence to be explained, nor any troubling female asymmetry or lopsidedness needing to be rebalanced.

It’s an attitude fuelled by the discourse around access to reproductive technologies that distinguishes the deserving from the undeserving via the malignant rhetoric of the “medically infertile” (heterosexual couples) versus the “socially infertile” (single women and/or lesbians).

This proposed defectiveness is what my daughter’s rejection of the two-mummy model challenges. Not that she knows anything of gender politics, homophobia or intolerance. All she knows is she has two parents who adore her—a Mummy and a Ma—each completely different and yet, together, sufficient and complete. I know this because when she pulls us both towards her into a three-way hug, shaking with the intensity of pleasure only a toddler can display, she announces with delight, “two!” Not two mummies, just two.

Samantha J Carroll is the stay-at-home co-mother of two adored girls under three. She also neglects two blogs (www.samcarroll.com and www.koalawrangler.com) and is writing her first novel.