Well you can point him at this post. I am a separated Dad, and been through the courts I cannot report any prejudice against me on account of my gender.
My situation is not what a lot of men experience as I have been hugely involved in the day to day care of my son, and demonstrably so. The bias in the courts is towards what is in the best interests of the children which is precisely where it should be imo.
Groups like f4j want to push for things like 50/50 shared care arrangements by default which I am not convinced is the solution in each and every case.
If as an advocacy group they pushed for cultural change rather than legal ones I'd support them in a hot minute. The change needs to be a wider acceptance of fathers taking primary care roles, and taking the hits to their careers in order to be more involved.
The root of the problem is not on unfortunate relationship break down, it goes back further than that with too many people falling into stereotypical gender roles.
The expectation of a lot of men flying forward in their careers, letting the mother take the financial/career hit and then STILL expecting a split down the middle when it comes to access is blue sky thinking when viewed from the child's perspective.
More men need to take responsibility for the consequences of their choices, and not blame biased court systems. More and more women have entered the workforce to maintain financial independence when relationships break down. The mirroring action for fathers is to take a greater interest in the day to day care of their children to protect their position.