Voted up because I like the attitude you show in your first two paragraphs.
However I think that you misunderstand the claims that you argue against.
Men have lower chances of having any kids than women
The obeservation underlying this is that that the average person has three times as many female as male ancestors. But every child has one male and one female parent. So the average male ancestor of now living people must have three times as many decendants as the average female ditto.
This might be because genocides were carried out by killing all men in a population, so that the women were forced to marry the conquerors. Or because two thirds of males that were born in some era were killed as children. Or because there was a tradition were some men killed other men's children, so that the surviving children had fewer fathers than the children that were born.
But in any case there was something going on that is not caught by your statistics. And the simplest (and nicest) explanation is probably that women got to choose who they had sex with, and some men were more attractive than others.
So why does your statistics say differently? I see two explanations off the top of my head. 1) Marriage, or in other words rationing of partners. Today each man marries one woman, and then other women are expected to marry another man and have at least one child with their husband. 2) Contraception, people have fewer children when they don't want children nowadays.
Also, I expect that if that study would talk about biological fathers rather than social fathers you would get different results.
Richer people, especially men, are more likely to have kids, and have more kids
Also, I expect that if that study would talk about biological fathers rather than social fathers you would get different results.
That's probably an important point, since some studies have claimed that a pretty enormous number of social fathers are not their kids' biological fathers.
I love seeing counter-evidence for everything. I estimate that while most of my beliefs are true (otherwise I wouldn't believe them in the first place), a small percentage is almost certainly completely false - and I don't really have any reliable way of telling the two apart.
Indiscriminatingly looking for counter-evidence for all of them can be very rewarding - the ones that are true are much more likely to sustain the assault of it than the ones that aren't. Yes, I might ignore counter-evidence of something that's false, or accept it for something that's true, ending up worse off, but it seems plausible that on average it should improve quality of my beliefs.
For example some of the standard beliefs about human sociobiology that seemed to be extremely widely held here are:
Charting Parenthood: Statistical Portrait of Fathers and Mothers in America disagrees with them.
These are not direct tests of sociobiological claims, so what we have is not exactly what we would like to, but I find them to be quite convincing counter-evidence. My belief in these sociobiological claims is definitely lower than before, at least as far as they concern modern world, even though I can imagine more focused studies changing my mind back.
More counter-evidence for things we commonly believe here, sociobiological or otherwise, welcomed in comments.