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So either Jesus is lying because he claimed in one place that you must eat His body (taking John 6 literally) as well as faith being all that's needed (John 5 and John 6 literally)
- or -

Jesus is talking figuratively throughout about being consumed. That we must take His teachings internal to us to change our hearts.

Or the more likely alternative:

You are constraining Christ to your punctilious, parochial, rhetorical standards.

For example, I've actually had people tell me the Bible has errors because God doesn't seem to know that bats aren't birds, as if the boundaries of modern species classification were written in stone at the foundation of the world.

The truth is God may not consider faith and works nearly as exclusive as you do. And by the way, that's the understanding of my Church.

I guess you can insist Deuteronomy 14 is bona fide error, but I don't think God will be too impressed by your reasoning...if for no other reason than I just explained it to you.

You are constraining Christ to your punctilious, parochial, rhetorical standards.

And you are not?

The truth is God may not consider faith and works nearly as exclusive as you do. And by the way, that's the understanding of my Church.

And then again, He very well may. See, there is not 100% provable solution here, nor a 100% agreed-to position. Thus it is dogma. It cannot be proven conclusively.

The Catholic Church teaches that salvation is by grace; it is not by communion or baptism. Thus the issue of transubstantiation - while interesting - is a minor, dogmatic issue.