The lack of evidence is one thing, but his argument contradicts itself.

He says that:

• the heavy investment that women make in their offspring means that they go to great lengths to make sure that their partners are committed
• we observe modern men killing their (the women’s) offspring in the expectation that those women will turn around and have children with them instead.

Apparently, the women failed to select fathers who would stick around to defend their offspring, and they’re happy to mate with men who kill the children that they have invested so much in. This strategy is clearly bad, so evolution would select against it.