That description does not contradict my words. It says about abolishing coercion and hierarchy, not authority

Edit: I re-read your reply. Yes, the part about being "against all forms of authority" is not entirely accurate, but the second part is true nonetheless. I suppose you could rephrase my example with the doctor and call it an "expertise" instead of authority, but the concept of it is people would still defer to specialists in specific fields that have more knowledge and experience than them.

As I'm new to the anarchism myself and do not wish to misrepresent its values, I think this this site might give you a better in-depth look

It's extremely telling that you are relying on Wikipedia for your understanding of Communism, rather than Marx, Engels, etc. You should read theory, if you want to start I made an introductory Marxist reading list.