You're right, that seems horrible.
This is actually why many of the disciples who followed him, stopped. (If you haven't already, please read all of John's Gospel, especially Chapter 6). It was a turning point. If someone asked me to eat their flesh and drink their blood I probably would have done the same.
- It sounds like insanity right?
The thing is, those dubious disciples really lacked supernatural faith that would have allowed them to trust Jesus despite the seemingly awful and awkward thing He demanded. They would have responded like Peter, to whom else shall we go. (John 6:68) Peter was the one of whom Jesus said regarding his Divinity "flesh and blood has not revealed this to you but my Father in Heaven," (cf. Matthew 16:17-28) and likewise, to the Apostles in John 6:63, It is the spirit that gives life; the flesh is of no avail. The words I spoke to you are spirit and life.
We can only trust Jesus by supernatural faith, and through that faith we can come to see the beauty of the Eucharist. This is something that goes beyond reason or even common sense; your brain can't get you to see this on its own. The problem that the disciples had then, and most people have now, is they imagine eating a dead person's flesh—an understandable product of the human imagination, but the reality is Jesus is giving His Whole Self: Body, Blood, Soul and Divinity from His Resurrected state in Heaven, which transcends space and time. His Body now is nothing like the body we can imagine, it is supernatural, holy, and like a nuclear bomb explosion of light. It is mind-blowing and cannot be perceived in its true state. It is not dead flesh, but the Risen Living Savior. He must veil Himself in the form of bread and wine because He would probably cause a lot of heart attacks otherwise.
But seriously, there are several critical reasons for the Eucharist, and many books have been penned over the centuries by saints and Popes to explain these realities. Here are just a few.
- Jesus is the Lamb of God, as so noted by John the Baptist, who was sacrificed to remit our sins. And just like the Passover meal in the Old Testament, the Jews had to consume the Passover Lamb to partake in the passing over of the death that was visited on Egypt. When we eat the New Passover Lamb, we are given eternal life with God in His Eternal Kingdom, far beyond what the Jews even hoped for.
- Secondly, you become what you eat. God wants to divinize us, to change us and transubstantiate us. He wants us to receive His Divine Life and become like Him, so His Heavenly food changes us on a metaphysical level. It is not something you can sense, but when you get to Heaven you will able to see what He affected.
- Third, the Mass is the representation of the Sacrifice of Christ: the whole paschal mystery made present to us, albeit in an unbloody form. We are transported to the moment when Jesus presents Himself to the Father on behalf of all of us, to redeem us and, at the same time, He grafts us to Himself and makes us part of His Own Body as if we are one with Him. It's like He has an all access pass to Heaven, and we are all with him so He gets us in. The Eucharist ties us to that pass.
You can also see the Old Testament figure of Melchizedek (Genesis 14, Psalm 110) who brought a sacrifice of bread and wine, which was a type of the Eucharist.
You could check out a lot of good books, but let me recommend one by my friend Vinny Flynn:
I hope this helps. I realize I am just scratching the surface of a very deep and rich subject, for it is the heart of our faith and an insane miracle.