The physical process of eating and digestion are being used as metaphors for a spiritual reality.
The argument against a strict metaphorical interpretation is that at no time does Jesus say that he is speaking metaphorically.
Initially, the Jews are scandalized. Jesus does not explain the difficult passages as being metaphorical. Rather, according to Scott Hahn, Jesus ups the rhetoric. Jesus begins to speak of "chewing" or "gnawing" His flesh. The Jews leave in disgust without a clarification from Jesus.
Similarly, the crowd leaves without a clarification from Jesus.
Even some of His disciples leave: "From this time many of his disciples turned back and no longer followed him."
Finally, it's down to the twelve Apostles, and Jesus, rather than explaining everything as a misinterpretation asks: "You do not want to leave too, do you?"
Only Peter (notably) speaks up and says: "Lord, to whom shall we go? You have the words of eternal life. We believe and know that you are the Holy One of God." Peter simply takes this "hard saying" on faith.
Additionally, Jesus normally explained his parables to the Apostles.
But to my eyes it seems that to read these statements as physical statements, saying that the material food becomes the material Christ is unwarranted.
For the record, the Catholic Church teaches that the earthly bread becomes the glorified body of Christ under the appearance of bread. (Since His glorified Body is not limited by time and space as is evident from Scripture, His Body can be in many places simultaneously.) In Aristotelian/Scholastic terminology, the substance of the bread changes while its accidents remain the same. The earthly bread takes on a supernatural nature.
In Catholic theology, Christ (acting through the priest) offers up His glorified Body (under the appearances of bread and wine) as an unbloody sacrifice to the Father. In a sense, Jesus perpetual heavenly offering of Himself to the Father is "brought down to earth." In another sense, it is a re-presentation of Jesus' sacrifice on the cross. His self-sacrifice on the cross is made present to us today, yet it is not another sacrifice.
Finally, the Scriptural and historical evidence for Jesus being the lamb of the Last Supper is very strong. In performing the Seder, it was essential that the lamb be consumed. Therefore, it follows that it was necessary to consume Jesus' Body when He performed the Last Supper seder meal ("this is my body," "this is my blood")
But was the meal completed? Note that Jesus does not drink from the cup at the Last Supper. He finally takes some wine just before His death on the Cross, and utters the words, "it is finished," meaning that the Paschal sacrifice is completed.
For Jesus' body to have been consumed at the Last Supper, Jesus must have been speaking of His Body in a sense other than his material body. It seems to necessarily follow then that Jesus' body was present in a non-material way in the bread and wine at the Last Supper for It to have been consumed.
This is the best explanation I've seen to prove how unbiblical transubstantiation is.
Heb 9:24-28 24 For Christ did not enter a man-made sanctuary that was only a copy of the true one; he entered heaven itself, now to appear for us in God's presence.
25 Nor did he enter heaven to offer himself again and again, the way the high priest enters the Most Holy Place every year with blood that is not his own.
26 Then Christ would have had to suffer many times since the creation of the world. But now he has appeared once for all at the end of the ages to do away with sin by the sacrifice of himself.
27 Just as man is destined to die once, and after that to face judgment,
28 so Christ was sacrificed once to take away the sins of many people; and he will appear a second time, not to bear sin, but to bring salvation to those who are waiting for him.
(NIV) Heb 10:11-14 11 Day after day every priest stands and performs his religious duties; again and again he offers the same sacrifices, which can never take away sins.
12 But when this priest had offered for all time one sacrifice for sins, he sat down at the right hand of God.
13 Since that time he waits for his enemies to be made his footstool,
14 because by one sacrifice he has made perfect forever those who are being made holy. (NIV)