One aspect of fatherhood that surprised me is what I call the 'rescue response'. I was not able to find any formal information about this behavior, but I have to think there is something out there.
I have experienced this exactly twice in my life on separate occasions: My child entered a physically and immediately dangerous situation. As soon as I saw their peril, my mind went into a kind of flow state. I didn't take time to weigh options, or consider any type of danger to myself, I simply reacted and before I could consider what was happening, I'd removed my kids from the peril. Later, in one case, I noticed I had bruises from my action. In the other, I received a call from the school principal.
Likewise, my father saved my brother and I from drowning, and I believe he had the same 'rescue response'. As soon as he saw what was happening, he dived in from the pier and swam the 30 feet to retrieve us, only to realize that once he had us, he had no idea what to do next. Meanwhile, my aunt had calmly climbed into a nearby canoe and rowed out to assist.
I don't claim this is strictly a father's behavior, or strictly a male behavior, but personally, I haven't had this identical reaction in the few times I've seen other peoples' kids in similar urgent peril. I have taken other action, such as alerting bystanders, but not immediately put myself into danger. I contemplated options first.