Considering the vast array of emotions triggered here, imagine the responses toward what Jesus said toward the end of John 6. Those who didn't understand Jesus, must have come away with some strange ideas.
And of course, the Jews were not allowed to even eat animal blood.
Maybe our Lord intended to divide those who took His claims seriously from those who did not. Those who strove with His words in a carnal sense were the unbelievers. Whereas those that laid up His words in their hearts would understand that they were to be taken spiritually, or would sooner or later understand that.
Look at how the Roman Catholic Church has taken up our Lord's words on this subject carnally long since the completion of Scripture.
We have a more intimate relation to Christ's sacrifice than the priests did in the Old Covenant, because we
both eat His flesh
and drink His blood, whereas the priests could not drink the blood of the sacrifices.
We eat and drink spiritually, symbolically, virtually and yet really, of course, and the Lord's Supper is a sacrificial meal in these senses.
It has nothing to do with cannibalism of course, as the Jews in John 6 and the Roman Catholics wrestled with.