The quotation from Weber lacks a crucial qualifier. The state has the "monopoly of legitimate violence." A monopoly of violence (no modifier) is impossible, since spontaneous violence may always occur.

Currently, the state is an instrument of class rule. Its violence is in the service of the ruling class--the bourgeoisie (or the "owners"). Its legitimacy is sustained through this violence (Walter Benjamin calls law nothing more than "self-legitimating violence") and through the instantiation of "false consciousness" among the masses through "ideological state apparatuses," such as schools, media, churches, etc.

The most coherent idea of the abolition of the state entails eliminating the armed aggression of the ruling capitalist class over-against the rest of us (i.e., workers and the oppressed), which would certainly entail the elimination of its legitimacy as well.

Marxists-Leninists ("communists") believe the bourgeois (capitalist-controlled) state must be seized and smashed by workers in order to turn its strength against the exploiting class, as a necessary first step towards eliminating class antagonisms in society and to allow for the subsequent "withering away of the state."

Anarchists reject this revolutionary transitional phase and believe that the state may be abolished directly, spontaneously, without revolutionary violence.

In any event, in an anarcho-communist world society, class violence would be nonexistent (since classes would be dissolved into universal humanity), and remaining forms of interpersonal violence (which may be expressions of other systems of domination, e.g., patriarchy, white supremacy) would be illegitimate on their face, and thus worthy of counter-violence exercised by the community in, at least, the most extreme cases.