This is kinda why I don't consider post-Left anarchism to be a useful concept (though I respect that @hakan_geijer , who identifies as post-Left, will disagree): hearing someone say "I am not a Leftist" is less about what that person's politics are than about how they define "Leftist."
It's like hearing someone say "I'm middle class." It rapidly becomes an argument about definitions, which is usually unproductive.
For myself, If I say "I am a Leftist", I'm saying that I'm willing to ally with communists and socdems because we have greater enemies in common. But you might have a different definition, and if we don't have that conversation then we rapidly become confused.