Anarcho-capitalism often thought of as "fascism looking for a leader".No, it doesn't say that. Anarchism exists on both the left and the right side of politics:
Issues in anarchism - Wikipedia
Left wing anarchists believe that anarchism removes hierarchies (namely the State, and hierarchies it supports and allows to prosper). Right wing anarchists seek removal of the State to allow those very hierarchies to flourish (in the same way that 'libertarians' argue for 'small Government' so they can freely racially abuse people and be free of regulations that stop them acting unscrupulously).
I'm left wing, and I oppose anarchism because I think the libertarians and right wing anarchists are onto something. If the State is removed and we're reduced to a state of anarchy (the Zombie apocalypse hits), the State is simply replaced with 'Mob Rule' and a 'Dog eat Dog' mentality, meaning the disadvantaged in society (women, ethnic minorities, religious minorities, homosexuals, the disabled, the poor etc) cop it in the neck.
'Every man for himself' does nothing to remove hierarchies; it just allows them to flourish.