i know men are usually not givin custody, but what statistical evidence is there to show that men are being descriminated against in family court when many believe men just dont care about raising children

for instance a comment i saw on twoxchromosomes on the topic that men apparently dont fight for custody anyway most of the time

Because to be frank, if a parent cares about their kid then they owe it to them to at least try. And because even though the court's biased it's absolutely not impossible to get joint custody: recent figures have shown that the instance of joint custody when a case is filed through court, accounts for just over half of post-divorce cases. Obviously, the bias is only gone if not half but all cases resulted in joint custody (well besides instances where one parent is actually unfit to parent), but! that doesn't mean it's currently futile when the dad tries.