To meet somebody's eye is to look directly at somebody who is looking at you. He would not meet somebody's eye.
Refusing to do it reads as guilt or shame, fairly or not. How long people meet somebody's eye differs between cultures more than almost any other habit.
1phrasemeet somebody's eyeTo look directly at somebody who is looking at you.
“She could not meet somebody's eye for the whole of the meeting.”
meet somebody's eye is a phrase.
Practised in Ways of Looking