Why is the head on the 1914 dime facing to the right and dimes after that face left?

Um, I don't understand what you are meaning. Barber dimes were struck from 1842-1916. All have their depiction of Liberty facing right. The Mercury and Roosevelt dimes all have the obverse head facing left. There is no real reason for that other than artistic preference. The Seated Liberty and Capped Bust face left while the Draped Bust coins face right. It is all just whatever the artist wants, there is no rhyme or reason for it other than artistic preference.