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The red part just says "when he had supped" So that would be after they had finished eating the famous Last Supper. Then he took the cup and show the apostles what to do. Doesn't say he drank from that cup. Though if Jesus did drink his own blood, who am I to stand in his way? It's Jesus' blood and he poureth it out as he pleases.
He thought 'supped' was past tense for 'sip', lol.
Another KJV misunderstanding. I think seminaries should do classes on the language of KJV. It would solve more misunderstandings than the Greek courses solve.