This dogma is one that non-Catholics have particular trouble accepting. However, we can see that the institution of the Eucharist is clearly revealed in scripture.
Before Jesus ascended into Heaven, He made a promise to His apostles, and to all generations “I am with you always, to the close of the age” (Matt. 28:20). To some, this presence refers to the Holy Spirit, which was received by the apostles at Pentecost. The Holy Spirit is one way Jesus has remained with us, to counsel and guide the Church. However, after being both bodily and spiritually present to His followers while on Earth, could Jesus only be referring to his continuing spiritual presence? Catholics profess and believe that Jesus’ continuing presence is physical and spiritual, as there is no greater way Jesus can remain with us than in His true flesh and Spirit. We come into communion with Jesus in this way during the celebration of the Eucharist.
During the last supper, Jesus declared that He was going to remain with his disciples under the form of bread and wine. In the institution of the Eucharist, Jesus consecrates the bread and wine with the words “this is my body”(Luke 22:19) and “this is my blood” (Luke 22:20). Jesus states this as an absolute, and is in no way left up to interpretation. In the next lines, Jesus institutes the priesthood with the words to His apostles “Do this in remembrance of me” (Luke 22:19). It is interesting to note, that the word remembrance in the Hebrew sense is not a word meaning “to recall a time in the past,” as it is generally used. Rather, the word remembrance means “to call forth the past into the present.” In other words, Jesus was instructing His apostles to bring this event into the present, which is what the priest does at each Mass.