"His brain has not only been washed, as they say. It has been dry cleaned."
--Dr Yen Lo (The Manchurian Candidate)
We seem to have reached a state where speech that someone doesn't like can be termed a 'micro aggression' that requires a 'trigger warning.' As laughably sad as that condition is, it does bid the question: When can speech be considered an act of aggression?
The short answer is rarely. Unlike physical acts of aggression where threat of bodily harm is at hand, people can avoid speech that they don't like by walking away or by tuning it out. Generally, because people have a choice to not take it personally, speech cannot be considered aggression.
However, there are few exceptions where speech might be considered an act of aggression. One is grounded in the well known saying that "you can't yell 'fire' in a crowded theater." The idea often attached to this claim is that an individual can't say something that incites a riot or panic that threatens people with bodily harm (such as sparking a stampede toward the exits in order to escape a fire). And it is true, in some circumstances such speech could be seen as an aggressive act.
But the fire/theater claim is often erroneous for various reasons. If people have the ability to process the speech, as in the case of incendiary remarks at a political meeting, then the speech cannot be considered an act of aggression. If the event is held on private property where the owners permit types of incendiary or disruptive speech, then the speech cannot be considered an act of aggression.
The fire/theater claim often gets the rationale wrong as well. Not only can a person not stand up and yell 'fire' in a crowded theater, a person cannot stand up and yell anything in a theater that might disrupt the ability of patrons to watch the show. The patrons have entered into contracts with the theater house and anyone that speaks loudly enough to disrupt the delivery of the service is aggressing against the property rights of the patrons and the theater owner.
This is the idea behind 'disturbing the peace' charges. It is also why people who attend political rallies to disrupt discourse between speaker and attendees are on dangerous grounds legally.
One other situation where speech might be considered aggression is where capacity to deflect offensive speech is minimal. Prison camps where propaganda is constantly blasted thru speakers at inmates is one example that comes to mind. Another is the case of children on the receiving end of ridicule by others (e.g., peers on the playground, parents). Because juveniles have yet to develop mechanisms for not taking harsh words personally, it can be argued that they are defenseless against such behavior, and that those directing harsh words toward them are committing acts of aggression.
Adults, on the other hand, generally have no right not to feel offended by speech because mature human beings are capable of controlling their feelings.