“There needs to be a way to create dialogue with them among the left.”
There isn’t. Once a movement accepts the use of violence for political goals, the only thing they agree with is employing more violence. In that regard it doesn’ matter what the politics are. All you can do in dialogue is attempt to persuade them that political violence is unacceptable, and shun and denounce them when they stick to their justification of violence.
I understand that this can be difficult when they espouse things one agrees with — even if it is in name only. But that is of critical importance. Just as it is the most undesirable speech that is most important to “protect”, it is the acceptance of violence within a movement that is most important for its members to counter.
The right has been denouncing the extermists who claim to be among them for decades (hint: otherwise there would not be an “alternative-right”). The left is again faced with leftist violence, and is again not denouncing it. But if “the left” wants to not be associated with it (and I’d certainly not blame them for it!), it must publicly, repeatedly, and unequivocally denounce it. Not only that, it should spend its dialogue energy on learning about the non-left through dialogue. This serves to bolster the foundation that we solve our disgreements with words, not violence.
“Why do they think they are in charge?”
Because the left is letting them be.
“I just don’t know how this could happen.”
First, we need to understand that what they (antifa) are doing is identity politicking. That is the first clue. Second, they claim they are “protecting” and “defending” against violence. But if, as the comments assert, it is the antifa faction initiating the violence, what are they “defending” against?
They base this claim on the phony notion that words are violence, that words of “hate” are indistinguishable from walking up and punching someone. That is how they justify their actions. This tells us how it happened: the left accepted the claim that words are violence.
The combination of “words==hitting someone” and “political violence is OK” only leads to real violence.