Yeah, the communication in that case is that you're letting the extremists know that your speech can't beat theirs, so you resort to violence. In other words, you're implying they're right and you're wrong.

It may feel cathartic and satisfy primal urges for retribution, but in the long run, 'punching Nazis' doesn't hurt the neo-nazi ideology, it helps it. Feeds the persecution complex, turns the guy you beat up who didn't physically attack you first into their martyr. Gives them more fuel to rally around and further radicalize them into wanting revenge.

Prioritizing a cheap, temporary thrill over real, lasting change for the better is ultimately self-serving, and not in service of your cause; ironically, it completely undermines it.

On a purely pragmatic/practical level, it's a bad idea, if your goal is to oppose Nazism.

Experts on extremism/terrorism etc. are all saying the exact same thing.

See for yourself: (emphasis added)

In the case of violent counterprotest tactics — e.g., punching Nazis — experts on extremism say it is likely only to aid the white supremacists’ cause.

The most commonly stated argument in favor of physically disrupting white-supremacist rallies is that society can’t give an iota of legitimacy to these groups. To allow them to spread their message of hate is to offer them a platform to recruit and to glorify their cause. What this logic leaves out is that it may well be the case that hate groups are better able to recruit and glorify their cause when they are able to engage in violence, regardless of how that violence starts, according to researchers in the field of countering violent extremism, or CVE.

“On the one hand, I don’t think these expressions should go unanswered,” David Schanzer, director of the Triangle Center on Terrorism and Homeland Security at Duke University, said of the recent white-supremacist gatherings. “But you’re essentially giving them exactly what they want when you try to confront them directly.” That’s because these groups’ efforts to recruit and mobilize supporters rely on a very specific strategy that benefits greatly from violent conflict.

In the U.S., explicitly white-supremacist groups know they are vastly, vastly outnumbered by everyone who hates them — their paltry numbers being an easy thing to forget in the age of social media and especially so this week, in the wake of a real-life white-supremacist murder. So their only hope for relevance is to maximize every potential bit of media coverage. And the best way to do this is to create media moments: scary, evocative images like the torch photos from last weekend, but also as many violently photogenic confrontations with counterprotesters as possible. Producing violence is an underlying, often unstated, goal of many white-supremacist protests and gatherings.

When violence does break out, videos of it race through the internet’s white-supremacist underbelly, serving as incredibly valuable PR material. It doesn’t matter who gets the better of a given confrontation: When the Nazis get punched, it’s “proof” that anti-fascists or liberals or [insert minority group] or whoever else did the punching have it in for “innocent white Americans just trying to protest peacefully.” When the Nazis punch back, it’s proof that their enemies are, to borrow a word from alt-right parlance, “cucks” who are easily bested in the streets. Even when white supremacists lose street fights, they win the long game.

This sort of tactic, said Jeffrey Kaplan, an academic researcher and the author of a number of books on terrorist movements, “is a constant in terrorism or any form of asymmetric warfare,” whether the group in question is jihadist or white supremacist or whatever else. Kaplan, who is an incoming professor at King Fahd Security College in Riyadh, summed up the extremists’ logic like this: “Our numbers are paltry, we are despised by our countrymen and we couldn’t get a date for the life of us, but any action that has enough impact to strike at the heart of the enemy by getting media coverage is a major triumph.” Violent confrontations allow extremists to make a tantalizing offer to the angry, disillusioned young men — they are almost entirely men — whom they hope to groom to become tomorrow’s haters and killers: We are part of a movement to change the world, as you can see from this latest video that movement is working, and you can be a part of it.

Schanzer laid out a fairly straightforward alternative: Counterdemonstrators should respond assertively, vociferously, and in far superior numbers — but at a distance from the extremists themselves. This tactic both prevents the sort of violent conflict American hate groups want, and has the added benefit of drawing at least some media and social-media attention away from the smaller hateful gathering and toward the much larger counterprotest.

“Violence directed at white nationalists only fuels their narrative of victimhood — of a hounded, soon-to-be-minority who can’t exercise their rights to free speech without getting pummeled.” “I would want to punch a Nazi in the nose, too,” Maria Stephan, a program director at the United States Institute of Peace, told him. “But there’s a difference between a therapeutic and strategic response.”

Even former white supremacists admit punching Nazis plays right into their hands, gives them exactly what they want:

...when mouthpieces for white supremacist ideology are physically assaulted on camera, it becomes a powerful validation of their victimhood complex: in their minds, plain evidence that white people are indeed under attack, and motivation to spread a call to violent response with renewed zeal. This “punch felt round the world” was a great boost to the “alt-right” cause. If you aid and comfort neo-Nazis, which is exactly what punching them in the face does, you are no better than they are. Real life isn’t a fucking Quentin Tarantino movie.

When I was a neo-Nazi skinhead over 2 decades ago, I got beat up as often as I beat anyone else up. It never made me any less violent. In fact, we used to pile into vans and drive from Milwaukee to Chicago for the thrill of brawling fellow devotees of romantic violence like the guy throwing the punch in this video. We lived for violent opposition. We thrived on it. Violence of any sort, no matter how it may be rationalized, is the bread of hatred. We put mustard on that shit and gleefully gobbled it up and clamored for more.

Back in the 1930s, there were gangs of communists who routinely brawled the Nazi brownshirts in the streets of Germany. Their contemporaries would have us believe that if there were more communists who brawled harder than they did back then, that the Holocaust wouldn’t have happened. As a former neo-Nazi, I can attest to how important it is to have violent opposition in order to maintain the hatred necessary to hurt people. The communist gangs helped Hitler’s National Socialist party come to power not only by galvanizing their own members, but more importantly by serving as a crucial ingredient in the overall atmosphere of fear and loathing that led the German general public to look to the Nazi party for order.