It seems when someone say "men", many people (including you) hear "all men". So, when I say men getting custody or being admired as an equal parent as women is a good thing, I don't mean all men. I mean the men who are really good at it, the men who are about petty masculinity, ego, and gender roles etc., and really love the child and the child's welfare is their first priority. So, most men aren't like that. We don't bring up men like that, mostly. And, then there are some biological factors, like mothers are the only natural parents, fathers have aquired parenthood, so how far they really can go as a collective to be an equal parent is still a big question. These simple things will be absolutely clear to you if you see the lifestyles of other animals (mammals) besides humans. There's no concept of father, it's just the females, males, their mating seasons giving birth to baby animals, female getting free natural resources, hence no depending on the male and no control or manipulation (patriarchy), females just bring up the babies till they are a bit old, babies go away. That's it. The natural/biological set-up. Now, fatherhood in our society was invented to privatize properties, patriarchy was invented through a mis-culture of violence and dominance (and that thing is not universal, in many part of the world, we had and still have matrilocality and matriliny, even some extent of matriarchy) pass down properties and money (again, unique to humans only) to father to sons. Nothing's natural about it. But what I was saying is that nowadays, many fathers are actually getting much support and fuel for thought, and successfully overcoming the shallow gender roles, truly becoming loving parents, which is wonderful. Custody (single, or, at least shared), alimony etc are justified in those cases, and those cases only. And the things have been gender-neutral in law since long. The percentage of fathers winning custody is naturally less, because most fathers are still very typical gender-role based ego-centric males, they won't even be able to bring up the children as good as the mothers can, they are out earning or doing whatever else they like to do outside most of the time, while a child needs attention. Or, many of these fathers battling custody are simply doing it to give their ex-spouse a hard time, foe their ego, and simply playing with the kids' future, some are violent and abusive, they don't deserve to be anywhere nrar the kids anyway. So, the percentage is naturally less. Now given that, sure, we, as a society have our bias, in very traditional and backward society, like Iran, Pakistan, Afghanistan (if at all, any woman wanting divorce gets out alive in this country) etc., grant custody of the children to the father, by law, and their society also largely think like that, heavily influenced by illogical religious teachings; similarly in liberal places, many people hold the bias that a mom should always get the custody of the children, even if the father is a really good parent. Now, these surely affect the percentage, in the traditional cases the laws are biased against women, and in liberal places, although the law is gender-neutral, the judges' mentality (specially if they are Republican) might not be, hence granting custody to woman who are in some cases not as effective of a parent as the father.
However, my original comment was about the patrilineal surname system, which is very absurd and biased, and I wrote almost an essay explaining why I think so, I put effort in that, so I would expect you read that, and come back with more detailed answer based on the points and not just write some emotional one-liner like "it's not selfish at all".
Lastly, I agree with the point Elle Beau made. Children from a single-mother Or two mother household (and similarly from a single-father Or two father household, however I noticed how your bias is only against the single or two mothers, and not the fathers) are don't lack absolutely anything in terms of the family structure, because as I said, motherhood is the natural parenthood (and an aquired parenthood, like fatherhood, also has the full potential to be as good as the best motherhood). However, I remember diacussing this particular point with you before too, where you were degrading single motherhood and lgbtq+ parenthood too. Lastly, your work with the lesbian parents' or the single moms' kids seem to have some personal agenda, as much as I understood from your comments. It seems one of the reason you work for that particular space is to confirm your internal bias that single or two mothers can not bring up their children normally, and that bias, if it's really present, is bound to affect the effectiveness of your work, and the children would suffer. A social worker is a gift of the society, so, I would really hope you think things thoroughly once and check your bias if it's there, and become truly effective. Thanks.