The claim that anarchism is chaos was refuted long ago by Alexander Berkman when he wrote: "I must tell you, first of all, what anarchism is not. It is not bombs, disorder, or chaos. It is not robbery or murder. It is not a war of each against all. It is not a return to barbarianism or to the wild state of man. Anarchism is the very opposite of all that" (Rogers 42). So, what is anarchism? All of the pro-anarchy sources I found say that, basically, anarchism is a political philosophy that embraces democracy and freedom, and seeks to destroy all forms of coercion and oppression. The root of human oppression is seen as authority and inequality (Bautista 249). This is why they think it is the perfect ideological guide for destroying poverty, racism, and sexism. All these oppressions are systems of power based on hierarchy. .
"Hierarchy means top-down, like a pyramid. Hierarchical constructions of power create positions of relative privilege and relative oppression. Capitalism, white supremacy, and patriarchy (male supremacy) are also top-down constructions of power. Anarchism conceptualizes power differently. Instead of power over, anarchism proposes power with, cooperation. This means that social systems and institutions should be based on cooperation and compromising. Power would rest in individuals and the collectives they freely associate into. Anarchism revolves around five basic principles: 1) equality; 2) democracy; 3) free association; 4) mutual aid; 5) diversity" (Rogers 34).
Equality can have many different meanings. In regards to the anarchist political philosophy, they speak of equality in reference to power. This doesn't mean they want a new society based on a totalitarian vision of everyone looking and acting the same. In fact they see strength in diversity. Instead they mean that everyone should have equal access to power, to determine how he or she wants to live his or her lives.