Jesus said the flesh, not my flesh. When he says “the flesh is of no avail”, he does not mean “my flesh”-that would contradict his immediately prior remarks. He means instead carnal understanding, as distinguished from spiritual(see John 3:6). The contrast is between unaided nature and nature elevated by grace.
If Jesus’ remarks are not to be taken literally, how would one reconcile 1 Corinthians 11:26-30? “So it is the Lord’s death that you are heralding, whenever you eat this bread and drink this cup, until he comes. And therefor, if anyone eats this bread or drinks this cup of the Lord unworthily, he will be held to account for the Lord’s body and blood. A man must examine himself first, and then eat of that bread and drink of that cup; he is eating and drinking damnation to himself if he eats and drinks unworthily, not recognizing the Lord’s body for what it is.” How could receiving a symbol or metaphor unworthily make one accountable for the body and blood of the Lord?