Why do people smash windows and set fires at a protest?

I think they think they can break the order. But the system is capable of responding to those anomalous behaviors.

Because the law and the govt allows them to.

Because they think that will make a statement against what is happening in the world.

As a resident of an area in the Twin Cities of Minnesota where that has happened, I have concluded there are two reasons. 

(1) Some of them are angry, frustrated, and upset at injustice, and they illogically express that anger in violence because they can't bear to bottle it up any longer. 

(2) Some of them are utterly disinterested in the protests, or actively interested in opposing them, but they take advantage of the disorder in the situation to indulge their own violent and sometimes predatory impulses. 

Regarding group (2) above, we've had two types here: The ones who systematically targeted drug stores and businesses with ATMs, looting them and then setting fires to cover their tracks; and the ones who are interested in undermining social order to further their own political agendas, including active white supremacists and anti-police revolutionaries. 

They are enraged and do not have the vocabulary or intelligence to express it via a positive route.

Job security for business owners...

N.Shadows

Been happening in America forever, here's a list for your review 

https://en.wikipedia.org/wiki/List_of_incidents_of...