How did Macduff convince Macbeth to fight?

Macduff did not have to convince Macbeth into fighting. Macbeth hears voices in his head that say he can only be defeated if the Birnam Wood "come to" Dunsinane Hill. He realizes that the prophecy may be coming to pass and goes after Macduff. As he enters the battlefield, Macbeth is certain he cannot be defeated. He refuses to fight Macduff at first and even taunts him to prove it to him that he was born of a woman. Once Macduff reveals the secret of his own birth (he was cut from his mother's womb), Macbeth is forced into the fight and is defeated.