The clash in Berkeley could be summed up as something like this:
Antifa: We're going to punch Nazis! This violence is self-defense!
Altright: We're going to punch you if you try! This violence is self-defense!
Antifa after getting punched/DarksydePhil: wowwwwwwwwwwww
This mess is the obvious conclusion of "punch a nazi! I'm captain america! going to collect 100 nazi scalps today my fellow comrades!" posturing. Normalizing violence isn't limited to one direction. The commonly trot out justification for violence against a demonstration/protest is that these words are implicitly causing violence, but what does that say of explicit threats of violence which manifest into actual violent disruptions done by masked individuals? The very same arguments that support antifa/black bloc/etc. are only more appropriate for their targets. The demonstration was an obvious taunt/bait in a very liberal area saying "you think we can't express our lawful rights and will use violence to enforce that" and Berkeley blindly rose to the occasion. If it's your "team" that is violently disrupting what would otherwise be a peaceful (albeit petty) protest, then if anything, the claim of self-defense isn't on your side in this case. That doesn't automatically apply to individual situations. I really don't know who was in the wrong in this situation with the girl, because both actors were pretty much out of the picture for most of it. It's obviously sympathetic to the victim of a punch, but the whole ordeal is such an ugly mess, you'd have to be a fool to limit the narrative to that little highlight. Outside one's innocence or guilt in a one to one exchange, why were people like her there in the first place is an important question.
What I saw in footage, including and beyond that small moment, was basically two gangs taken from a shitty version of The Warriors going at it (with more innocent participants, with more of these obviously being with the original demonstration, staying back unless they got pulled into it). Both sides (ohmygod, I said both sides! that means I instantly lose!) have developed a hero complex where they are defending the good cause (saving hypothetical minorities from hypothetical genocide by bashing neonazis clad in a mix of Rome fetishism and channer memes vs. protecting free speech from anarchist cosplayers who cover themselves with various commie iconography they bought with Amazon Prime), but it isn't hard to see this is all a bunch of bullshit to excuse some id-driven thirst for violence. Revenge fantasies involving smashing people with sticks built up in echo chambers, now being acted out in real life. Alt-righters saw a fairly benign woman get maced by a masked individual at a Milo protest and started getting ideas how next time would be different. Chris Evans saw questionable woman get socked in the face and now wants to meet the guy (who seems like a basket case) who did it in person to fuck him up. What a bunch of vulgar garbage. Celebrating political violence is so lame and it has led us to this. It's a shame the cops were fairly useless in this situation.
As for GAF, they are playing a fairly obvious game - I mean besides just focusing entirely on an inconclusive clip. It involves yelling "BUT HE'S A NAZI" as an answer to any and all concerns about political violence. You can see it pretty well with this post by FyreWulff:
bwahahahaahahahahahahaha
Neonazis want all non whites killed or quarantined, women as broodmares, run themselves like a gang, and execute those who try to leave ("blood in blood out")
antifa is anti-sexism, anti-racism, and anti-classism. While they are critiqued for being really aggressive, trying to butbothsides antifa is irresponsible and basically going "why do you care so much about fighting Nazis".
At the very least, a significant amount of people who attended the event don't believe this. They are just dopey trump voters, libertarians, or even something further left who have a bone to pick with college campuses. That didn't stop people from throwing various things, including even bricks, into the crowd.