> That's simply the continuation of a societal expectation that women will do the 'mothering.'
You are ignoring biological reality. The reason why this happens in 'hetero' couples is that the woman has an obvious physical relationship with the child. This doesn't happen in gay male couples because neither of the fathers can have this relationship. In lesbian couples, it's common for the non-bio mother to not only feel alienated, and even to do less childcare than the biological one (https://www.thespermbankofca.org/sites/default/files/1998_Ch...). Lesbian adoptive couples are more likely to share childcare equally, just like gay male ones of any kind, or heterosexual adoptive families.
My wife and I used to be really into this idea of parental equality in all things until we had a baby biologically. Now I obviously love my daughter, but there are some things only a mother can do, like nurse her, and this forms a special bond between mother and child. The fact of the matter is that men have to work harder to get that close of a relationship with their child that the mother is predisposed to. However, even then, the most devoted father would likely still see their child want to nurse when they get hurt or feel scared, until the child reaches 2-3 years of age. This is normal. Nursing is meant to do this, and although it's a physical act, it has real emotional consequence in both mother and child. My heart breaks hearing my daughter cry, but my nipples do not leak milk. It's not even that I couldn't calm her when she's mad, but the fact is that it would take significantly longer. Meanwhile, the child will be screaming and upset, and I should be willing to do this in the name of equality? On the other hand, handing her off to nurse with mom calms her instantly, as nature dictates.
To me it seems cruel to force my view of equality on the child by forcing them to remain terrified, frightened, anxious, and sad all because I want to feel as important as their mother, even while mom is right there. Is this unequal? Certainly. But it is the only humane decision in our opinions.
That is not to say we should think less of paternal love or the paternal relationship (especially since research shows that dads play a very important role in socializing their children into larger society), but rather that we should not see the inequality between mom and dad especially with young children and attribute it to some nefarious social force, instead of millenia of biological reality.