It is said in the Mass "Calvary is made present", and the same sacrifice of Christ's flesh and blood is "re-presented" in an "unbloody manner". What was offered at Calvary was the sacrifice for sin, of which Christ said as He was about to give up the Ghost, It is finished. He finished the sacrifice for sin upon the moment of His death because death was the payment for sin. Since that death occurred, the payment is paid in full. To perpetuate what He clearly finished is eating the sin sacrifice, the sacrifice of the dead. Christ had instructed at the Supper that its elements of wine and bread were "memorials" of His death (do this in memory of me). A memorial of an event is not the actual event, but a reminder, as are all memorials. They remind about something that happened at one time. When He said, This is my body, or my blood, it is no different than pointing to a dot on a map and saying, this is Louisville. Is the dot Louisville literally? Or does the dot represent Louisville? When we point to a photo and say, this is my son, is the photo the literal son, or a representation of the son? We often use such expressions to say things are certain objects with the understanding they aren't literally those objects.
Furthermore, the Supper is a Thanksgiving sacrifice, thus "eucharist". Under the laws of Moses, the sin sacrifice and the thanksgiving sacrifice were two distinct sacrifices. What kept them separated was that with the sin sacrifice, there could be no leaven present; while with the Thanksgiving sacrifice, a leavened loaf had to be included.
The Thanksgiving sacrifice could not be offered if the sacrifice for sin were not finished. Christ's flesh and blood was the sin sacrifice for His people. For this reason, on the night of the Supper, He commanded them that from that point they were to offer the sacrifice of Thanksgiving, which is the meaning of "eucharist". No Jew of that day would have mistaken the "eucharist" as the sin sacrifice.