Another story says the expression began in the theater.
New actors shaking with fright were told that the only cure was to go out and face the music.
The music was played by the orchestra seated in front of the stage.
A similar expression is face up to. It means to accept something that is difficult or painful.
For example a man must face up to the fact that he lied about the business deal and will lose his job.
Or a child must learn to face up to her responsibilities and complete her schoolwork.
Meeting someone face-to-face can be exciting, especially if the other person is famous.
It is an expression one may use after visiting the White House and meeting the president face-to-face.
Or a teacher might ask for a face-to-face meeting with the parents of a student in trouble.
It means to talk to someone in person, not by telephone.