So this is the crux. The world is upset because while Trump decried the actions of both sides, he didn't decry the ideology of the side that is fundamentally anti-American and anti-human, which antifa's basic anti-Fascist ideology is not. Actions vs. ideology is a crucial distinction and in my view is the responsibility for the President to make verbally (and far more important, actually believe). In addition, those towing the "both sides at fault" line should make it too IMO.
Moreover, many people have empathy (if not support for) using violence to stop the potential coalescence or spread of an anti-American, anti-human ideology. You object to that empathy, but I do understand that perspective, though I may not agree with it.
Like you, I am a staunch anti-extremist if for no other reason than extremism on either side becomes totalitarianism at a faster and faster rate the farther one moves down the stringency curve at either end. Anyway, fair enough -- we understand each other though we may disagree.