It is understandable that in moments of stress he might react strongly.

If a person does illegal things, a paedophile for example, it is forbidden to take the law into your own hands. It is police matter no matter how angry you are.

If he is being habitually bullied the correct way to deal with this is to make an official complaint, gather evidence and consider legal action to get a restraining order.

If someone attacks you or your property you may well say they have a retaliation coming, and so they do, but it must be proportional. To punch the offender might be proportional in the heat of the moment (a court might give you a discharge perhaps a conditional discharge), but running after them and threatening to kill them would be disproportionate and leave them open to serious charges. That could be construed as abuse.