Look people, you gotta be real careful with this one. I'll show you two of the problems in the dataset, there are many more than two problems.
First off, lone fathers abuse their children at a much lower rate than lone mothers. By "lone" I mean the classical single parent situation with no other adult in the family. It is true that there is a lot less child abuse in lone father families. That said, the group lone fathers does not in any way match up with the group lone mothers. It is much much harder to become a lone father. That creates a partial filter.
The group lone mothers includes drug addicted young women who have a very high incidence of child abuse: These particular women change their boyfriends like they change their underwear. Unrelated males who have no attachment to the child, the child's mother or to child rearing itself have an atrocious rate of child abuse. There are almost no lone fathers who fall into that pattern and unrelated females with no attachments have a lower (still dangerously high) rate of child abuse.
The group lone fathers and the group lone mothers are too different to compare directly!
Next, the group "fathers" as used in studies often includes the mother's boyfriend. This artificially raises the rate of child abuse in the group fathers. We must be extremely careful to see exactly what is being measured when reading these studies!
Note: the feminist "women spend more time with the children" is a red herring. When time with the child is the prime factor there is no child abuse difference between the sexes. Fulltime stay-at-home dads do every bit as well as fulltime stay-at-home moms.
The reason there is more maternal child abuse than paternal child abuse has to do with the factors I discussed above when speaking of lone parent families.