The symbolic turning together in the same direction harkens back to the Early Christians who often prayed facing East, waiting for the second coming of the Son of God, like the rising of the Sun....In offering Mass facing toward the people I have often thought how strange it is that I would be praying to God while I was facing you. Think of that: you all face in the same direction together (toward the altar, the cross and the Eucharist), as you pray to God. So then why would I face you while I'm praying to God, and leading you in prayer and presenting your sacrifice to God. Facing with you always seems more natural, more prayerful, more uniting.Read the article; it's worth the few minutes and may enrich your understanding of the Church's wisdom. Incidentally, Vatican II did NOT mandate that the priest face the people, and, in fact, that posture is a clear temptation to say Mass a performance of the priest rather than as a sacrifice to God.
Here's a video of the Novus Ordo as it could be: