Women have custody of children more frequently than men, and women who have custody are more likely to also be awarded child support, than men who have custody. These are statistics for my country but I believe they probably apply broadly.
Source.
Part of that probably has to do with some real statistical behavioral differences. In other words, the huge split isn't just due to court bias. So, it can very well be the case that women are more likely to want custody, to deserve custody, etc. But it does seem to be an uphill battle for men, and so when they argue that they are discriminated against on the basis of gender in custody court cases, I sympathize. Men are often less trusted around children in general, like there are often ads for babysitters that explicitly state a female preference.
For a specific case, my father lost custody of me at age 4 to my mother, despite the fact that he was more qualified to have custody of me. So, seeing the statistics, and then seeing one clear real world example, makes me sympathetic to the idea that men face discrimination regarding child custody, and lots of other things related to children as well.