If you can't find any good reason in your setup to justify his behavior, it means that that rooster is rotten and should not breed. We should breed for good birds that are doing their best to pass their genes, not for jerks who tries to extinct themselves.
A rooster that attacks his own chicks and his own girls is not tolerable. There are so many good roosters who need a good home, there are zero reasons to keep a rotten one and breed more chickens with these bad genes.
This said, my own, so far perfect rooster got an inch from getting culled on the spot after permanently crippling one of his own 3 day old kids and killing another one.
I saw from the window the rooster, grabbing one chick while the broody hen was distracted, shaking it like a dog, and tossing it in the air. I penned the chicks and had to go to work, and when I came home, I found another chick out of the pen, flat dead. Certainly this is rooster's doing.
I was so furious and ready to kill that rooster when someone on this forum suggested me to think 10 times before killing such good rooster.
So I tried to get inside the mind of this rooster and I tried to understand his reasoning behind what he did, if there was any... And I realized it was all my fault.
Due to my setup, chicks younger than 6 days tend to get stuck either outside or inside the coop.
The broody hen was not experienced so that might also be a factor to her losing chicks here and there.
The chick that the rooster crippled was stuck outside the coop and couldn't get in, and the one that got killed managed to escape the pen that I didn't secure enough, and got stuck out of the pen away from his mother.
When a chick starts getting agitated, and the mother gets agitated, the flock also gets agitated, and the rooster has the duty to stop agitation and keep peace in the flock. The only way the rooster had to stop the agitation was to make the agitated chick shut up, by killing it. Better a chick dead by rooster than his whole harem dead by a fox. He can always make more chicks in his reasoning, which is perfectly coherent with nature's law. Losing a chick is not as bad as losing a laying hen. It's probably a defense mechanism to not attract predators, because a screaming chick and an agitated flock is obviously a predator magnet.
So yeah, I fixed my setup and never had this problem again. Since then, my rooster has been wonderful with both chicks and broodies.