Transubstantiation as held by the Roman Catholic church states that at the Eucharist, which is the regular taking of the emblems of bread and wine, these emblems become the real body and blood of Jesus Christ. Proponents of this view believe that mystically Christ is sacrificed again and transformed into the local bread and wine. As a result of this denominations, that believe this, typically do not allow ordinary parishioners to serve themselves, but rather a priest or member of the clergy must officiate.
Proponents of transubstantiation arrive at their conclusion based upon the words of Christ in Matthew 26 and elsewhere in the gospels:
And as they were eating, Jesus took bread, blessed and broke it, and gave it to the disciples and said, “Take, eat; this is My body." Then He took the cup, and gave thanks, and gave it to them, saying, “Drink from it, all of you. For this is My blood of the new covenant, which is shed for many for the remission of sins." Matthew 26:26-28
Christ uses the actual words for eating and drinking in these texts. Roman Catholics therefore take Christ's words in the most literal sense and believe that the bread became Christ's body and the wine His blood. In addition when Christ says do this in remembrance of me the literal application of the body and blood of Christ in the emblems carries over and Catholics along with some other Christian denominations believe that Christ is crucified afresh.
However this view based upon a literal understanding of the retelling of the last supper has conflict in other passages of scripture. For instance in Hebrews the author states:
For such a High Priest was fitting for us, who is holy, harmless, undefiled, separate from sinners, and has become higher than the heavens; who does not need daily, as those high priests, to offer up sacrifices, first for His own sins and then for the people’s, for this He did once for all when He offered up Himself. Hebrews 7:26,27
According to this text Jesus offered himself once for all for sinners on the cross. No further sacrifice was needed. Thus we can conclude that the concept of crucifying afresh our Lord every time we partake of the Last Supper is at odds with the aforementioned selection. This section of scripture is not the only text at odds with this interpretation: 1 Peter 3:18 also makes it clear Christ suffered only once.
Christ also stated in the Sermon on the Mount that if the right eye offends to pluck it out for it is better that one part of the body be cast off than for the whole body to be thrown into hell. Of course very few Christians take this advice literally and understand this to mean that we need to do whatever is necessary to guard the doorways to the soul.
The connection of transubstantiation to corporate justification follows in that the arguments to support both are similar while these concepts deal with very different ideas. Proponent of corporate justification believe that Christ legally justified the entire world at this death. In elaboration this means that every person has been justified by Christ's death whether they are in a saving relationship with Him or not.
One of the texts used to put forth this belief comes from 2 Corinthians 5:
For the love of Christ compels us, because we judge thus: that if One died for all, then all died. 2 Corinthians 5:14
Expositors of corporate justification explain that since Christ died for all and all means every person that has ever lived, every person that has ever lived died when Christ died. The problem with this view of course is that while Jesus physically died the rest of the world did not physically die at this time. Thus while Christ obviously died on the cross the rest of the world did not obviously die. Therefore the obvious understanding of the text is not possible.
The reader is left to conclude that there must be some other way to understand that Christ died for all and subsequently all died. Proponents of transubstantiation believe that Christ becomes the bread and the wine and in a similar way proponents of corporate justification believe that all the people of the world died when Christ died, but in both places this does not work with the flow of the texts.
In the case of the Lord's Supper Christ had not yet been sacrificed in any way and He claims that the bread and the wine were His body and blood. As a result this obviously cannot be true. Christ must be using the bread and the wine as symbols. In the case of Christ's death on the cross Christ died while no one else died (that we know of) when Christ gave up His spirit. Thus when Paul says that all died in Christ it must mean that everyone vicariously died through Christ's death. When we vicariously do something we are doing it through someone else while they actually experience the action.
Paul goes on to say in 2 Corinthians 5:
He died for all, that those who live should live no longer for themselves, but for Him who died for them and rose again. Therefore, from now on, we regard no one according to the flesh. Even though we have known Christ according to the flesh, yet now we know Him thus no longer. Therefore, if anyone is in Christ, he is a new creation; old things have passed away; behold, all things have become new. 2 Corinthians 5:15-17
The argument carried forth is that Christ died that others might live. The emphasis on this substitutionary death of Christ is on the living and those that are in Christ. While God wishes that none would perish not everyone chooses to die with Christ or to experience His death vicariously.
In conclusion there are many metaphors that God uses to explain what happened at the cross. Just as Noah's ark was large enough to physically save the world at the time of the flood so to was the sacrifice of the cross large enough for everyone to be saved. But only those that got on the ark where saved and only those that take up the cross with Christ through a willful cognizant choice will be spiritually saved.