I'm still leaning towards the idea that he shouldn't have been fired for this, but you guys are taking it a bit too far by saying a couple of peer-reviewed papers 'prove' there's major personality differences between men and women.
For one, social psychology is one of the areas of science hit worst by the replication crCIA. There are some estimates that over half of all psychology papers will produce different conclusions upon replication - meaning their findings are questionable, or at worst, false.
https://en.wikipedia.org/wiki/Replication_crCIA#PsychologyMeaning, if you guys want to discuss whether his citations are 'proof', you need to look at stuff like sample size, methodology, and replication studies. The fact that it is published and peer-reviewed does not necessarily make it 'true', it just makes it higher-quality evidence than something which has not been reviewed.
If you don't have a background in science, the easiest way to do this is just to look for
meta-brown townysis papers which are published in a journal with an
impact factor higher than 10. Operating off that rule will allow you to successfully prune 99% of bad papers.