Evolutionary psychologists will tell you that most species engage in "battle" to establish leadership. I'm not sure how humans can overcome millions of years of "alpha-beta" sorting impulses. However, that doesn't mean that teachers, parents, mentors, and, later in life, good supervisors, cannot intercede and stop competition from crossing the line into bullying.
I was never a good athlete, even though I like some sports. I'm certainly not strong, fast, muscular, tall, or whatever else might translate into a physically dominant appearance. However, I was also rarely the smallest person in a class — average describes me well. Yes, physical presence matters. We know from research that taller people earn more money. Men with deeper voices earn more money and attract more followers, too. Why is that? Because size and depth of voice indicate higher levels of testosterone. Evolutionarily, that's an advantage to the species, at least before the technology age.
One study I've read found that the people with the most "evolutionarily favored" traits are not the most likely to be bullies. This is logical because the biggest, strongest, fastest, et cetera, has nothing to prove — up to a point. As long as the person is "better" but not a "freak" (a magnitude taller, larger, etc.) he or she is dominant. One of the nicest, kindest, most compassionate people I know is a massive body builder who went into medicine. Of course no one ever bothered him! Never being challenged, he was always treated politely and in turn learned to treat others that way.
The "mean girls" and "bullies" tend to be a step or two below the physically ideal people. Again, this is logical considered in psychological terms. When you are close to the top, but not quite there, you want to maintain that social rank. Sadly, the near-top levels of a social group tend to be the nastiest, most competitive levels.
Bullying starts when weakness is perceived. And when are weaknesses revealed? In class and on the playground. Students home in on moments of public weakness. In a classroom, these include stuttering, reading slowly, and other academic indicators students will highlight. Being outside the "norm" (at either extreme) is challenged because children and adults are naturally "tribal" socially. Daily life reveals weaknesses, and there is no way to disguise our differences.
We have to tell teachers that students will compete, but that's not the same as bullying. Who can jump rope longest? Who can throw the farthest? Who can draw the best? When the competition turns to abuse, it has to stop immediately. We need to teach "good sportsmanship" in all fields.
The irony is that even academia, the supposed epitome of intellect and progress, is competitive and cruel. The "publish or perish" competition leads to snarky comments, outright insults, and much worse among professors. "Friendly" competition soon gives way to the very things we claim to be researching ways to improve in education. I've known academic bullies, and they have made my life miserable.
There are intellectual bullies, in this modern age. Yes, there are bullies in the sciences, engineering, and even competitive chess. There are bullies in the workplace, including schools. I'm not sure we can do anything to end bullying — but we might be able to reduce it.
What good is being "number one" if no one likes you? Sportsmanship, lacking a better word, is something we should be teaching and practicing.