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:

Men have lower chances of having any kids than women
Richer people, especially men, are more likely to have kids, and have more kids

Charting Parenthood: Statistical Portrait of Fathers and Mothers in America disagrees with them.

It's true that young men are less likely to have children than young women, but it reverses at old age, and total chance of having children during lifetime is - for people over 45 - 84% for men, and 86% for women. As some of childless men might still have children between 45 and their death (quite a few according to data), but almost no woman will, the difference must get smaller by the time of death, or it might even reverse. This is pretty convincing evidence against a major gender difference in chance of having children, at least as far as modern America is concerned.
The chance of having children is highest for people between 100% and 200% of poverty line (poverty line, not median income, these are all poorer than average people). For women going either lower or higher reduces chances of having children considerably. For men getting poorer reduces chance of having children considerably, while getting richer reduces it but only slightly. However - younger people are much more likely to fall below poverty line, and men tend to reproduce later, so even that can easily be an artifact of age-income relationship. The data is fully compatible with both poverty and wealth being negatively correlated with chance of having children in both genders.

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.