Why Do Catholics Believe in Transubstantiation?

Many people that object to the Catholic belief that they receive the Body and Blood of Jesus Christ forget about the Last Supper (See Luke 22:1-23) and the Bread of Life Discourse (See John 6:22-71).

At the Last Supper Jesus tells His disciples in reference to the bread "this is my body, which will be given for you" (Lk 22:19).  Non-believers in transubstantiation claim that this is the only time in which Jesus' body was consumed as the sacrificial lamb.  Yet Jesus was sitting right there with them as the bread that became His body was given to them.   He did not pull some flesh off of His body and give it to those at the table, he turned the bread into His Body.  In John 6:52, the Jews questioned this when he was teaching in the synagogue in Capernaum (Jn 6:59), "The Jews quarreled among themselves, saying, 'How can this man give us [his] flesh to eat?"  Jesus replies in John 6:53-58:

"Jesus said to them, 'Amen, amen, I say to you, unless you eat the flesh of the Son of Man and drink his blood, you do not have life within you.  Whoever eats my flesh and drinks my blood has eternal life, and I will raise him on the last day.  For my flesh is true food, and my blood is true drink.  Whoever eats my flesh and drinks my blood remains in me and I in him.  Just as the living Father sent me and I have life because of the Father, so also the one who feeds on me will have life because of me.  This is the bread that came down from heaven. Unlike your ancestors who ate and still died, whoever eats this bread will live forever."

Continuing in John 6, some of the disciples questioned Jesus "Then many of his disciples who were listening said, 'This saying is hard; who can accept it?'" (Jn 6:60).  Jesus rebukes them, but it was still difficult for some to understand.  "As a result of this, many [of] his disciples returned to their former way of life and no longer accompanied him" (Jn 6:66).  Then we are reminded of eternal life in the Kingdom of God (Jn 6:67-69):

"Jesus then said to the Twelve, 'Do you also want to leave?'  Simon Peter answered him, 'Master, to whom shall we go? You have the words of eternal life.  We have come to believe and are convinced that you are the Holy One of God.'"

All believers in Jesus Christ are called to receive the Body and Blood of Jesus Christ to have eternal life.  His Body and Blood could not simply be available once.  Otherwise only those at the table of the Last Supper could have participated in the reception of the Body and Blood of Christ.  So the end of Lk 22:19 "do this in memory of me" is not a command to offer bread and wine as a symbolic offering, it is in fact the offering of the Body and Blood of Jesus Christ, who was sacrificed for us at Calvary.  This is difficult for some to comprehend.  If one can see the offering of bread and wine at the Last Supper as being His Body and Blood even though He had not yet been crucified, they should be able to see that the priest is in fact offering the Body and Blood of Christ just as Jesus Christ Himself did at the Last Supper.  Although He died only once for us, His Body and Blood are not limited to time.