Mothers try to help. Fathers hang back a little and encourage the child verbally or physically to bear the frustration and stick with the task. When a child learns to ride a two-wheeler, dads are more likely to put a child back on the bike after a failed attempt. Mothers slow and simplify speech for preschoolers. Fathers use bigger words, longer sentences.
Children are more compliant with the same gender parent.
This reinforces over the years. When a child's behavior is undesirable, mothers tend to emphasize the social and relational costs, to mention shame or disappointment in being personally let down. You'll never find a job if you act like that. Infants 7 to 13 months respond more positively to dad lifting them than to mom. Fathers carrying children tend to hold them face forward.