This cannot be resolved, you will not be an equal parent or even close to it the first few months, maybe even over a year. Breast feeding and various dependencies that develop (like that the kid wants to fall asleep at the breast) mean that most of the effort of parenting early falls on the mother.
And then there's the fact of life that other stuff needs to be taken care of. Trash still needs to be taken out, groceries bought, etc further pushing you towards the stuff outside of parenting.
This can hardly be resolved with money. We could hire nannies, get the top nursery, whatever. It would even be cost-efficient if it let mom work. However, the kid doesn't want to be without his mom and much more so she doesn't want to be away from him for a longer time! Even with me 4-6 hours is about it.
Very few men lactate, that is absolutely true. However, in our family it is the mother who has the drive and career ambitions, which is why the child has fallen asleep on the father instead, including when said child was but a few months old and the mother had a six-week business trip abroad.
I am sure children benefit from having several parents and role models, but I am not so sure that the shape of the genitals matter as much as whether the parent(s) is/are emotionally in tune with the child. The classical father of yore was simply not much of a parent. Today's can choose either.
That is true for a few months. You have children for rather longer than that. Even with breast feeding you can express the milk. I did that. I used to work from home with my younger daughter asleep in a sling.
Your child might want the mother, but this is no true of every child. Different kids in the same family can be different in this way too.