I don't think fighting back is shitty in any way.

a) Either there is no objective morality and then anyone can do anything they can justify using their personal moral system, as long as it's internally consistent (it blatantly isn't for most people and perhaps subtly isn't for the rest)

b) or there is objective morality and then anyone can dispense punishment (for example by fighting back) because there's no reason the objective morality would favor a given person over any other.

The idea that people should not solve their own problems or other people's problems stems from:

- People in positions of power wanting to justify their power, thus indoctrinating everyone into believing they need protection. The more authoritarian the state, the more restrictive guns laws. Authoritarian teachers demanding absolute order and children punishing each other is disorder.

- The difficulty of ascertaining who the original aggressor is and who is just fighting back.

- The likelihood of people making mistakes and punishing the wrong person of overshooting the level of appropriate punishment.

- Internal conflict weakening the whole groups, making it more susceptible to outside aggression - better to punish both sides fighting to keep order and appear strong.

All of these have some merit in some situations and to some extent but IMO none of them justify their logical conclusion - total submission to a supposedly unerring position of power.

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But back to fighting back:

I've seen two groups of children - those who were encouraged to fight back and those who were encouraged to endure it or ask teachers for help.

You don't see the first group bullied much so you might not even identify the group as a target of (potential) bullying.

Meanwhile I have never seen the second group's strategy working out - the bullying always escalated until a breaking point.

Additionally, from what I've seen, when the second group changed strategies to fighting back, the bullying stopped.

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Finally, another pattern I see emerging from personal experience is that the parents of the children involved often know each other because they went to school with each other, even if not necessarily one class. And the parents of aggressors ("bullies") behaved the same way. The behavior absolutely is transmissible and I don't believe it's solely through social means. Some anti-social personality traits have a large genetic component and these traits are often a major cause of the need to hurt others.