Voilence isn't necessary and in the long run you may know the actions of a person by the fruits of their shortcomings. But here's why it poses as a good short term solution. 

It can empower said person, or state, or faction. It's a tool/method that's capable and readily used within the spectrum of human behaviour. It's not always a necessary "evil" because quite frankly if the US invaded a Polynesian island with voilence, the natives rising up in arms would leave them worse off than if they simple sat with their thumbs up their backsides. Why? Because the threshold of how much power over your environment voilence can supply is much lower for the natives than it would be for the US. 

But say the US was going against Qutar, and instead of using militant means to fight against the US, Qutar simply said "cheap oil" to either the US, or someone with equal militant strength. The war ends with a snap. Was their voilence? No. But there was a gained position in power. 

It's not voilence that solves the problem, it's the ability to disempower the conflicting party through which voilence provides that matters, and you can do this with other means than voilence. It's less "should voilence be fought with voilence" and more "How do I achieve a position of power equal and/or higher than that of my opponent, and what traits to I currently have that would do so.". 

Asking a 90lb bookworm to go fisty cuffs with a 200lb jock is retarded. 

The problematic duality that we hold that "voilence is neccessary because alternatives" don't always work is because the alternatives we have in a competitive based world is bullshit. Economics is built in a way that naturally breeds conflict of interest and will manifest into seperations, segregations and divides of all kinds. It's an exclusionary based profit model. It's why you'll see countries war it out, and it's why you'll see those same values of "dog eat dog" power play trickle down our cultural ladders to the playgrounds. Alternatives like open discussion and more altruistic building exercises are great in building bonds and allowing people to disarm without feeling vulnerable. But when dealing with a bully you're already dealing with someone who still feels vulnerable in these kinds of situations, who still values power as it's more prioritized in his set of adopted cultural values, and is reflective of repeated exposure to environments where he probably has to utilize or abide by these social presets. To say "hey now be friends, hold hands and let's talk it out, school is a safe place, go make daisy chains" is all nice and good, but at most cases it won't work because the bully won't see any need to change his behaviour and his current behaviour will still probably be re-enforced elsewhere. 

So, in order to beat the bully without using voilence, you must do it in a manner that comes from a position of power, something he recognizes. After his submission, which is hard again if he's exposed to conflicting environments, will you be able to better handle remoulding his behaviour to one that's more altruistic and representative of an egalitarian, open culture.