Using the verb of being does not, by itself, settle whether a particular analogy is literal, figurative, or something more exotic. Jesus also says He is the door of the sheepfold. Is he merely apparently human in form, but in the deeper reality a physical door? You place too much weight on IS in isolation. Language simply doesn’t work that way. Lots of moving parts, and they all have to work together to arrive at legitimate meaning.
For example, you ask why the people of John 6 suddenly wanted to part ways with Jesus over this. If you would look closely at the response, it provides a giant clue to aid in understanding what he was really saying:
Joh 6:61 When Jesus knew in himself that his disciples murmured at it, he said unto them, Doth this offend you? [62] What and if ye shall see the Son of man ascend up where he was before? [63] It is the spirit that quickeneth; the flesh profiteth nothing: the words that I speak unto you, they are spirit, and they are life. [64] But there are some of you that believe not. For Jesus knew from the beginning who they were that believed not, and who should betray him.
Do you see what happened here? They were repulsed by Jesus’ words because they did not think of them in a spiritual sense, but in a literal, material sense. Jews could not eat human flesh, and God would never command them to do that. But they could not get to the next level of understanding. Jesus says specifically that it is the spirit that gives life, that the flesh profits nothing.
Keep in mind He speaks this in a context where his own literal flesh was the subject of discussion. He is deliberately deflecting his listeners from attaching any importance to the notion of consuming his physical being in some literal sense. He wants them to think of it as a spiritual transaction, not a fleshly one. And then He caps it off by stating the reason why some cannot get to that spiritual understanding; they do not believe, which is tied to the earlier statement he makes near the beginning of this exchange, that only those believe whom the Father has drawn to Him. So he closes the loop, using the inability to comprehend the spiritual nature of his atonement as a live demonstration of the earlier statement about the necessity of being drawn by the Father.
Might I suggest you take a look at the earliest of Church teachings and discern whether they believed in the real presence of Christ in the Eucharist?
The teachings in the first century are extremely clear on the presence of the Lord in the Eucharist. Seriously, read those who likely were Catechized by those who walked with Christ.
Well stated. One of the best I’ve seen.