As I recall, fathers are discouraged from seeking primary custody without strong justification (by the advice their divorce lawyers give them, by not being able to afford a divorce lawyer at all, by the fear of losing all access to their kids if they kick up a fuss...) so the cases where they do seek custody are going to be biased towards ones where the mother's abusive or otherwise unfit. The study doesn't seem to investigate whether this is the case.

Also, I'd be interested to see actual methodological details. For instance, it talks about women being unable to get adjustments in payments to which they're entitled. Did they bother to investigate whether men have the same problem? They don't mention it if they do, and anecdotally they do seem to have difficulty getting their payments adjusted down if they lose their job and can no longer afford to pay as much. To be honest, I reckon this study is kind of biased in terms of what questions it actually asks.