A "nihil-ist" is a label in reference to the emotive reaction to what is being reacted against, in this case, reaction of alienation to perception that reality has no ground, ie if reality has no ground, then all is without meaning. In this case, the "I" becomes its own God because, without ground, it is its only ground.
An anarchist is someone focused on societal structures, in this case an assumption that an absense of strucuture is "good", itself based upon an assumption that all hierachies, pathological or not, are "bad" and inherently coersive. In this sense, the "I" of the anarchist is defined by the authority he is against, rather than being predominantly orientated towards formulating a solution beyond structure. But this is not what the anarchist does - look for solutions - because his recoil is directed towards authority rather than its transcending; he defines himself by what he against, and that action of thge mind prevents him, in its operation, from looking to what we all could be. Do you know any anarchists who pose evolutionary solutions that lead towards the world of other-to-other that they say they want to go towards, or is it just bitching? It is not utopian if a movement towards a utopia is not made.
On reaction, I think you are responding to what I said on the other thread where we are talking. Please refer there.