This is but mere biased definitions, the truth for which the power fears anarchy is total different, this is why they portray it as violent, violence is not anarchy, is but mere organized chaos.
Anarchy is organized mutual respect and support.
And in that case there is no need for a structure of power.
And that my friends means that there is no need of Putin, or Clinton, or Bush or Thatcher or Assad or Trump or Obama or Saddam or anything similar, and that scares the shit of all the psychopaths in power, army, politics, business, for that takes the most desired toy out of their hands, absolute power, dominance, control, despotism, dogmatism, their power over their own kin.
Study a bit the history of anarchy, there were anarchic cities in Italy that lasted and prospered for hundred of years, same in antique Greece, until military organized greedy psychopaths warlords from exterior conquered them to loot them, just go ahead and study this, it is really interesting.
And that is why they call any negative event now Anarchy, that is why they send violent Black lives matter, or other smashers in the midst of any peaceful protest, to make it look like thieves are looting and destroying everything around when seen on TV, than call them anarchists, but they are not, mostly they are police or military in action under cover and under strict orders to create chaos and destruction so they can blame anarchy... and the demonstrators.
Watch them carefully any demonstration, the organized chaos agents only destroy a small area where preventively is all the press filming (by some odd chance), than the police block opens miraculously for them to pass through unharmed, smiling at each-other, than they simply vanish.... in thin air (actually they put the police gear back on and are to be found right there under shields charging against the real demonstrators).
Because they love chaos, and promote it, than label it anarchy so nobody thinks that anarchy is good.
That is not anarchy.