This may have been covered by others in this thread at this point, I haven't read through it all. If we are talking men in the aggregate, we can look at the sorts of play that boys are more likely to engage in. There are of course boys and girls that defy the averages, and any natural division is likely enhanced by cultural expectations. However, there is strong evidence that boys and girls tend to lean toward certain activities.

Boys like to take part in competitive activities, often physical in nature. There is a joy in testing one's limitations and relative capability compared to others. This can often take the form of fighting each other, acts of violence toward inanimate objects, or imagining combat scenarios. None of these are exclusive to boys, but again boys tend toward it more often. Add in the effects of testosterone, and you get a predisposition toward aggressive, physical acts if that is what we define as violence.

However, if we define violence using a criminal definition of violent crimes, then we must ask if men are more likely to lose control or willfully commit acts of violence. The more recent evidence of DV and SV point to parity or near parity in rates of inter-gender violence. For men vs men, we see a higher level of physical violence, which would support the idea that men are predisposed toward physical violence. I say physical, because we could also look at emotional violence (harder to measure or track), and there is evidence that women vs women violence is much more likely to be emotional in nature.

So in the aggregate, we may be able to say that men are predisposed toward one type of violence toward men, women are predisposed toward another type of violence toward women, and each have roughly the same rates of violence toward each other.

To the point of your question, I think the narrow view of violence that we tend to have is hazardous to men. We police harshly physical violence without putting as much effort into addressing emotional violence. At the same time, efforts to reduce physical violence in adults end up suppressing the physical types of play that boys are more likely to derive joy from. The result is we have a skewed negative view of men and generations of boys that feel penned up and that their love of violent competition is wrong.

On a side not, part of the value derived from that type of play is gaining an indepth understanding of what one's body can handle including pain. So part of the process of growing up for boys is generally getting hurt and learning to tell when the pain needs to be addressed and when it can be ignored.