An "Armchair critic" is an idiomatic phrase, it's similar to the idiomatic phrase "Armchair philosopher". These idiomatic phrases tend to carry a negative connotation. They usually mean a charlatan, or someone who is "all show and no go" An "Armchair critic" is someone who criticizes things without an understanding based on experience, it can also mean someone who criticizes without trying to help.

An armchair critic is someone who expresses opinions about things they know very little about. There views are "in theory" other than first-hand experience. Ex: That guy on tv is such a armchair critic! He just watches t.v., and takes credit for things he never has tried.

I just saw this expression in a comment. I exactly don't know its meaning!

What's the context? A chairman is the person who leads ('chairs') a meeting or a panel of experts etc, a critic writes reviews of books, restaurants etc. I suppose a chairman critic might be the leader of a panel of critics?