It means nothing.

I was thinking about my earlier answer. Given that I see it was Shakespeare who wrote it, I really suspect it means the following: As a love interest for a woman, or as a leader of others, "An average man is not the right man.". Or said differently, why settle for average?

I think it's just philosophical, so there's no meaning on the surface that every English speaker (even native) could comprehend right away. So you have to guess it, it's a quibble. I guess you have some of those in your language too, in your poetry or writing.

I have never heard of the two phrases put together this way, but English speakers are always creating new, poetic or sarcastic terms. An everyman, which is one word not two, is an average man. It literally means to have the characteristics of all men. To be a no man has two meanings: 1 - to always say no to questions or ideas, 2 - to not have the characteristics usually associated with men of good moral character. I suspect this term is saying that the person is "an average man with no moral character" .

such a person*