If there are two groups (and in addition they are roughly equal size) those are entirely interchangeable as there is no logical "standard" to compare to except eachother
Imagine if there are 200 people, 100 of category A and 100 of category B. It's possible for members of category A to be simultaneously "liked more than average" and "disliked more than average". If 20 A's are liked and 20 A's are disliked, while only 10 B's are liked and 10 B's are disliked, then A's are liked 33% more than average and disliked 33% more than average.
I think it's more naturally interpreted as a frequency question ('given a random A, how likely is it that I would say "I like this person"?') rather than an average/sum question ('what is the total likability of all members of A minus the total dislikability of all members of A?')
The fact that men are specifically feared for some imbalance, whereas women are specifically valued for others, makes it not exactly interchangeable even if the standards only exist in a relative sense. In the hypothetical world, men (and perhaps women) would place extra value on women due to the way sexual desire and attraction works, but men would be seen more neutrally (or with disinterest rather than fear) than in our situation.
I'm not sure what research you are pointing towards, but I sincerely doubt that the propensity for violence is identical, either. Consider the following scenario: a person points a gun to your head and tells you to pick a person at random either amongst all of the women or amongst all of the men (let's sidestep the question of gender neutrality for the sake of the argument) If the person you pick has an aggressive and violent psychological profile, you are shot. Which gender would you pick in this situation to maximize your survival? Would you sincerely rely on your intuition about equal capacity for violence in this case?
Let say you wrote a AI that detected if a person talks negative about a other person in order to make themselves look (or feel) better. We run this AI over a messenger network with true identities. Will men or women be tagged proportional more often?
An other example, let count the number of bullying victim in schools and number of people who are guilty of committing bullying. Will it be boys or girls that are found guilty more often?
A person who wields a gun is more like male because people who own and wield guns in this culture is male. If the person were a poisoner, statistics will say it is a woman. Why? Culture.
What research on violence say is that violence is defined by culture, and if the violence we highlight is those typical of male culture then that is the kind of violence we see. For a very long time researcher did not even consider that female-female competition existed among animals because the only form of competition researcher know of was defined in term of male-male competition. It was only in recent decades that they realized that, in contrast to previous theories, females do compete with each other that mirror the violence seen in males. It just happens to be very different form of violence, although the consequences were often just as deadly as male-male competition.
Let's say we take the cultural argument at face value. If the capacity for violence is identical, why did we come to have a culture that fears men more or highlights male violence? Why were researchers blind to female-female competition in the first place? The explanation is that the violence in question has a dimension of brutality and assertiveness towards challenges that goes beyond just classifying it as male or female and leaving it at that in a cultural relativist sense. If it were completely equal, it would have been very unlikely that we would have assigned such lopsided values to these types of violence since no tradition or cultural expectation is completely divorced from material reality.
In the jungle people find a dead young female baboon. She is apparently dead from starvation, so we hastily conclude it was natural causes. The researcher however who observed the flock gives a different explanation. The young female was healthy just a few weeks ago, but after joining the flock she got continuously bitten and scratched by other females whenever she went to eat or tried to sleep. After weeks of constant stress, lack of sleep and food she died.
In contrast we might find a dead young male baboon clearly beaten to death. They joined the same flock recently and after a large fight over dominance the young male acquired injuries and died. Which of the two cases displayed more capacity for violence, brutality or aggressiveness? Is a brawl better or worse than cold calculated murder?
> why did we come to have a culture that fears men
Very good question. One likely answer is that we have a culture that reward men who commit violence in the right context. Why do men get rewarded for violence? There are many contradicting theories and books on that subject. Are humans inherently violent or peaceful? Is society holding back the savage beast or is cooperation the human default behavior? A lot of questions, a lot of research, a lot of theories.
If you want to dig down into those question there are good books and other sources on it. The stanford Human Behavioral Biology lecture serie on youtube is a good start (https://www.youtube.com/watch?v=NNnIGh9g6fA&list=PL848F2368C...). The same researcher has also a book called Behave: The Biology of Humans at Our Best and Worst, which focus a fair bit on aggression and violence. There is War Before Civilization: The Myth of the Peaceful Savage, which also has a counter-argument book which name is currently evading me.
This is also true for basically all large social mammals (cats, dogs, deer, ...), and seems to be a consequence of the fact that female parental investment is greater than male parental investment. In situations like seahorses where the male paternal investment is greater than the female, it is the females that are bigger, stronger and more aggressive.
Size, strength and aggression are directly related to capacity for violence. Men are bigger, stronger and more aggressive, and therefore have a higher capacity for violence. This is why we separate men and women for e.g. boxing or MMA.
An other easy question. Let have two human households, one where two men live together and one where two women live together. Which one is more likely to have domestic violence?
Based on biologically, those two should have a very clear and simple answer. The actually answer is that two female dogs are more likely to fight than two male dogs, and in human households, both of them has statistically identical rates of domestic violence.
EDIT: Note the sarcasm. We are, in fact, a thing.