"I'm so mad at the government that I'm gonna smash some stranger's business!"
That train of thought indicates either utter stupidity or agents provocateur, not consistent anarchist philosophy. Consistent anarchists don't try to imitate the State. Rioters is not a synonym for anarchists. Violent chaos is not anarchy, it is indicative of a desire to control others without the sophistication or veneer of tradition employed by governments.
Rioters and vandals often attack the elements of society that promote peace and prosperity through trade. The labels they claim and slogans they chant are irrelevant, because they still use the political means of plunder rather than the economic means of production.
Politics is parasitic by nature. Civilized society is its host. A human without a tapeworm is better off than a human with a tapeworm. Tapeworms don't cure other diseases. Look at the world around you. Every voluntary association and exchange in your life is anarchy in practice. While we live in a world with politicians and police, they are not responsible for civilization. Government is not society. Governments wage wars. Governments build police states. Politics creates chaos and violence. There is nothing magical about the services government has monopolized that immunizes them to the faults of monopoly. Elections don't actually produce representation for the governed. Politicians are not endowed with special knowledge or virtue by their office. Instead, the consequences of their ignorance and vice are unrestrained by the need to gain consenting customers.
People choose instead to cooperate in peaceful ways because it creates a win-win opportunity for everyone. We disagree perhaps on how we prefer to associate, but without the zero-sum game of politics, we don't need a single socioeconomic system any more than we need a single church denomination. Of course, one can always expect to be asked what we would propose instead of government. Abolitionists didn't need to explain how to harvest cotton, tobacco, or sugar to say slavery was wrong. All we need to say in response today is that consent is superior to coercion, and the real consequences of central control schemes are more dangerous than the liberty bogeyman.