Is Christ in the Eucharist?

The Jews asked Jesus what sign he could
perform so that they might believe in him. As a challenge, they noted that “our ancestors ate manna in the desert.” Could Jesus top that? He told them the real bread from heaven comes from the Father. “Give us this bread always,” they said. Jesus replied, “I am the bread of life; whoever comes to me will never hunger, and whoever believes in me will never thirst.” At this point the Jews understood him to be speaking metaphorically.
Non-Catholic Christians say that in John 6 Jesus was not talking about physical food and drink, but about spiritual food and drink. They claim that coming to him is bread, having faith in him is drink. Thus, eating his flesh and blood merely means believing in Christ.
But Jesus first repeated what he said, then summarized: “I am the living bread which came down from heaven; if any one eats of this bread, he will live for ever; and the bread which I shall give for the life of the world is my flesh.” The Jews then disputed among themselves, saying, “How can this man give us his flesh to eat?” John 6:51–52
His listeners were stupefied because now they understood Jesus literally—and correctly. He again repeated his words, but with even greater emphasis, and introduced the statement about drinking his blood: “Truly, truly, I say to you, unless you eat the flesh of the Son of man and drink his blood, you have no life in you; he who eats my flesh and drinks my blood has eternal life, and I will raise him up at the last day. For my flesh is food indeed, and my blood is drink indeed. He who eats my flesh and drinks my blood abides in me, and I in him.”John 6:53–56
Notice that Jesus made no attempt to soften what he said, no attempt to correct “misunderstandings,” for there were none. Our Lord’s listeners understood him perfectly well. They no longer thought he was speaking metaphorically. If they had, if they mistook what he said, why no correction?
On other occasions when there was confusion, Christ explained just what he meant. cf. Matt. 16:5–12 Here, where any misunderstanding would be fatal, there was no effort by Jesus to correct. But he knew some did not believe. (It is here, in the rejection of the Eucharist, that Judas fell away; look at John 6:64.) “After this, many of his disciples drew back and no longer went about with him.”John 6:66 If it had all been a misunderstanding, if they erred in taking a metaphor in a literal sense, why didn’t Jesus call them back and
straighten things out? They would have remained with him had he said he was speaking only “symbolically.”
But he did not correct these protesters. John 6 was an extended promise of what would be instituted at the Last Supper—and it was a promise that could not be more explicit.