Some Reasons to Deny the Physical Presence of Jesus' Body in the Elements of the Lord's Supper

And when He had taken some bread and given thanks, He broke it and gave it to them, saying, "This is My body which is given for you; do this in remembrance of Me." And in the same way He took the cup after they had eaten, saying, "This cup which is poured out for you is the new covenant in My blood. (Luke 22:19-20 NASB)

In general, the faithful Christian should be cautious about taking any kind of "just me and my Bible"
approach to forming convictions concerning the Faith. The Lord Jesus established a community of believers and He appointed teachers within that community. We should have humility to learn from the past generations of the faithful.

On the other hand, Christians who self-consciously hold to the principles of the Protestant Reformation must declare that the Bible is necessary, authoritative, sufficient and clear: Scripture alone is the final authority regarding matters of faith and practice. Other authorities are composed of men who are fallible and subject to error, while God's Word is perfect (cf. Psa 19:7): infallible and inerrant.

And so, though major streams of religious tradition that self-identify as "Christian"–and, indeed, perhaps the majority of actual followers of Christ throughout the ages–have believed that the physical body and blood of the glorified Christ are somehow present in the elements of the Lord's Supper, the first and foremost examination regarding this issue should not take place on the basis of human history books or opinion polls, but on the basis of the biblical data.

In regard to the words from Jesus, quoted above, one must note:

1. Jesus does not use the verb "become," but the simple verb "to be" [in this case, "is"].
2. In other passages, Jesus uses the verb "to be"in ways that are clearly metaphorical–ways in which "become" clearly cannot be supplemented to it–no one, for example, argues that Jesus became a literal door when He declared "I am the door" (John 10:9).
3. Likewise, in Luke 22:20 (repeated in 1 Corinthians 11:25), the words “This cup which is poured out for you is the new covenant in My blood” cannot be taken literally, “for clearly the cup itself is not actually the new covenant;” “Paul means, rather, that the cup represents the new covenant inaugurated by Christ’s blood. Similarly, when Jesus says that the bread 'is My body,' it likely means that it represents what Christ has done on behalf of the church through his sacrifice." (Schreiner, New Testament Theology)
4. In reviewing Jesus' institution of the Lord's Supper in 1 Corinthians 11:23-26, the Apostle Paul quotes Jesus as twice saying: "Do this in remembrance of Me." This seems to point to the character of the Lord's Supper, not as a partaking in ingesting the physical body and blood of Jesus, but as a memorial feast, antitypical of the Passover (see below).
5. The Lord's Supper clearly has its background in the Passover: in the Passover there is no thought of the bread and wine becoming the body and blood of the sacrificial lamb.
6. In the cultures to whom the Gospels and Epistles were addressed (note Paul's comparison between the Lord's Supper and idol feasts, 1 Cor 10:21), there was no thought of the elements in religious feasts becoming the physical body and blood of a deity/religious figure.
7. If the Lord's Supper was meant to involve the physical presence of the body of Jesus in the elements, therefore, this aspect of the Lord's Supper would be a point of explicit contrast to both the Passover and to idol feasts; in order to make this point of contrast clear to the earliest church, more explicit instruction would be required from the apostolic writings.

Traditions that teach the physical presence of Jesus' body in the elements invariably neglect the implications of the fact that the glorified Christ is currently seated at the right hand of the majesty on high, having completed His gospel work once and for all (cf. Psa 110:1; Heb 1:3; 7:27; 10:10-14), and they make the Lord's Supper not just a crucial corporate proclamation of the gospel, but a part of a gospel-obscuring (at very best) sacerdotal system.

[See:

Peter Gentry, “The Lord’s Supper BF&M Article 7b,” An Exposition from the Faculty of the Southern Baptist Theological Seminary on the Baptist Faith and Message 2000 (Louisville: The Southern Baptist Theological Seminary, 2001), 25-28.

Thomas Schreiner, New Testament Theology: Magnifying God in Christ (Grand Rapids: Baker, 2008), 730-734.]