The knights of the Middle Ages were often violent, illiterate, lustful, and predatory. One can find plenty of examples of their bad behavior. Yet the ideal they officially aspired to was a knight who was gentle, wise, respectful of women, and a defender of the poor. And there were knights who actually incarnated those values (William the Marshall, to take one easy example). So, yes, men being men can be awful pigs; but men can also be noble and self-sacrificing and builders of a better society while employing the same traits in a better direction.
The patrol method in Boy Scouting was consciously founded on what is called the gang principle. Boys like to run together, taking their cues from each other while engaging in energetic and risky endeavors. Such a group, if it gets into petty thievery and vandalism, is what we call a "gang" in the usual sense. A better-directed group can find joy in service projects and camping in the woods. You take the innate, the ineradicable behaviors of boys and give them a better goal to aim for. It's still a gang, but in making it into a patrol, it becomes something admirable rather than deplorable.
The same thing can happen with team sports. Yes, we all know athletes who behave badly. But they don't behave badly because they are athletes. And what the coach values (and tolerates) has a great deal to do with how athletes behave. It's not about aggression or energy or competition, all of which can be good things. It's about morals. It's about a vision of the good. And for many men, their experience in youth sports was a good one with many lasting good effects upon their character.
When you define masculinity itself as toxic, you wind up telling boys to be like girls. Besides being doomed to failure, this simply alienates the boys and makes them less likely to succeed and more likely to misbehave. And behold, your hypothesis of "toxic masculinity" seems to prove itself. But what if you did what teachers and coaches and clergy and scout leaders have done for generations, and tried to direct the masculinity before you toward goals that require energy, aggression, competition, risk-seeking, etc., and which can only be reached by discipline and the adoption of proper values? In other words, what if you endeavored to make Men out of the male creatures before you?
But to do that, you have to have a vision of what a Man is. You have to know what masculinity can yield, and not merely define it as toxic, no matter what it does. And that is probably beyond the capability of the doofuses and bewoke scolds who currently hold the microphone.