Whenever I think of an analogy to help non-Catholics (and even poorly formed Catholics) to better understand why Jesus instituted the sacrament of the Holy Eucharist I like to share it. Here is one I think might help some.
Many Christians yearn for a "personal relationship with Jesus" and to "know Jesus in a personal way." Ironically, when the Holy Eucharist is sanctified, it is exactly as if Jesus "in person" is knocking on your apartment or house door. People who do not partake in the Holy Eucharist are deliberately not answering that door, often at the same time they are sitting inside either wishing for a personal relationship with Jesus or bragging about their personal relationship with Jesus! Hmm.
Jesus knew he would be missed. He said so. He sent the Holy Spirit to strengthen heart, spirit and tongue to proclaim the truth and know God. But he also instituted the sacrament so that people would have Holy Eucharist to comfort them while he has gone. He said that too. So whenever someone partakes in the proper reverential way in the Holy Eucharist, they have "opened the door" to Jesus personally and in reality knocking on their front door.