I'm not going to get too deep into the nature versus nurture argument. I have no doubt certain aggressive tendencies are inherited, but I’m also sure how the rooster is handled as a chick and an adolescent has a lot to do with magnifying or minimizing those tendencies. You are in a totally different situation than I am so I can’t be of any real help to you on that based on my experiences.
I may be able to help a little on how a cockerel matures. Each one is different and on their own time scale, so I can’t give you an absolute schedule, more of a sequence.
Even at hatch some cockerels have certain tendencies. Not all, but some. They tend to have a more upright posture and are more curious. They tend to have more personality so of course these are the ones people tend to fall in love with. A lot of cockerels don’t exhibit this at hatch, but many do. And the pullets can exhibit a lot of this behavior too. It is really difficult to be sure of sex based on behavior at hatch, but occasionally you get a cockerel that you know from the start.
As they mature their behavior changes. This can be as young as a few weeks or it can take months. The cockerels continue to be the leaders. If you open the pop door from the coop to the run, the first ones out are more likely to be the males. The first ones to even look out are more likely to be male. Again, some pullets will surprise you but the leaders tend to be male.
At some point, often 12 weeks to 16 weeks, the male hormones attack. Again, it can be younger or much later. They start to show an interest in the opposite sex, while the pullets are generally much later in showing any interest in this. That can cause for some stressful times in the flock and for you as you watch. But most of this interest is not really in sex, it’s about dominance. Those hormones are driving the cockerel to become THE flock master, the most dominant chicken in the flock. They start fighting and trying to intimidate each other. They also try to intimidate the pullets, to show their dominance to the pullets.
The sexual ritual is about dominance as much or maybe more as sex at any age, but especially here. The one on bottom is accepting the dominance of the one on top, either willingly or by force. At this age it’s force. The pullets are slower to mature and don’t know what is going on. It can get pretty rough and messy.
To complicate it a bit, the pecking order is also being established. Pullets may square off and fight cockerels as well as each other. Pecking order has a lot to do with maturity, the more mature will rank higher than the immature of either sex. Since the individuals of both sexes mature at different rates, there can be a constant resetting of the pecking order until they all grow up.
At the end of the day you will wind up with one dominant rooster, monarch of the entire flock. The rest of the flock will sort out their pecking order. It’s not that unusual for some of the hens to outrank some of the non-dominant roosters in the flock. Things really do get peaceful.
There are no set ages when any of this occurs. Some people report a cockerel trying to crow at one week of age, some wait until they are seven or eight months old. That shows how much variety there is in this. From what I’ve seen in my flock, most cockerels start serious male behavior around 12 to 16 weeks. Depending on flock make-up as well as their own personality, this behavior can last a couple of months or maybe as long as a year. I’ve had a rare cockerel acting pretty mature by 4 to 5 months, but some have taken all of a year. Typically things settle down around 6 to 7 months. Most pullets are laying by then so they have finally matured and the males have pretty much sorted things out between themselves.
The one that is most likely to become human aggressive is the flock master, the one that wins all those battles. He is the one with all the responsibilities of the flock on his shoulders. It’s his job to protect the flock. He also has to continually defend his position as flock master if there are any challengers. If he hears a hen in distress, say someone is chasing them or catches one and she is protesting, he will go to see what is going on. He may or may not defend that hen. If he perceives someone as challenging his position as flock master, he may attack.
I remember a post in here several years back where a 5 year old boy saw a rooster dancing for a hen, so he went out to dance for the rooster. It was so cute, until the rooster attacked the kid. That rooster had been fine with kids, never a threat. But when that kid danced for him, that was perceived as an attempt to dominate him, take away his position as flock master. Remember the mating ritual is about dominance as much as sex. From then on whenever that rooster saw that kid, he attacked.
It’s things like that that can trigger a normally great rooster into suddenly attacking, his flock being threatened or his position being threatened. You never know what is going in in the mind of that rooster, what may set him off. Some people have noticed that their rooster attacks them when they are wearing certain colors or certain shoes, but are fine otherwise. Some roosters may leave you alone but attack any stranger.
It is certainly possible for a family and a rooster to coexist. I grew up on a small farm with a free ranging flock, always with at least one or two roosters. I don’t remember me or any of my four siblings ever being attacked but those chickens were not pets, they were livestock. We worked and played in their vicinity but never went out of our way to interact with them, except when I’d chase one down for the dinner table. Others on here have serious problems with roosters.
I don’t know if you will get anything beneficial out of this or not. I don’t think I told you anything about how to avoid a problem. Good luck!