Does John 6 teach that the Eucharist is the real body and blood of Jesus?

Roman Catholicism loves to use part of John 6 to teach that you must "eat His body and drink His blood" by eating the bread and wine of the Eucharist.

But is that the context of the passage? What is really going on?

There are a few problems with this view. One - it is teaching cannibalism which is forbidden in Jewish Law. Two - it ignores the context which makes it clear that Jesus is being hyperbolic and metaphorical because the crowd were misunderstanding continually and so He is mocking them. Three - it hides the real message of the passage and the Biblical gospel that "eating his flesh" and "drinking His blood" for eternal life means hearing and believing, and coming to Him.

We start with John 1 and walk through John 2, 3, 4, 5 and 6 to show the context and what the Gospel of John is teaching in those chapters that is relevant to this.