An important concept that helps to make this possible is AristotleÕs idea of Òaccidents.Ó These are not the modern ideas as in a Òbus accident.Ó In the hands of the Creator, you see that the substance of something is very deliberately being manipulated. These teachings were later developed and Christianized by Sts Augustine and especially Thomas Aquinas. They are not hard to understand, but take more time to explain than I could possibly muster. Besides, as a Catholic, I understand I do not need to reinvent the wheel. I am currently reading Anthony RizziÕs Science Before Science, which, though not explicitly a history of the beginnings of the natural sciences, shows quite clearly how they come from Catholic culture. This is getting way off topic (though I strongly suggest that anyone who can read words purchase this book). The important thing is that though we are regarded as illogical and suspicious, there is Divine irony in the fact that Catholic culture gave us the science later generations would use to try to disprove the Real Presence.
To get back to the topic, we have to point out that the reaction of non-believers to the Real Presence in the Eucharist is exactly the same as that of the Pharisees and other hard-line Jews when Christ proclaimed His divinity. To explain the concept of Real Presence, briefly, it is different from Divine Omnipresence. When God resided in the Old Testament Tabernacle, He was really there. At the same time, He did not relinquish His Omnipresence – His total reign of the created universe. But in the Real Presence, just as in the Tabernacle, we have the type of presence that is the same as meeting Christ in person.
This is whole idea of our worship. It is the focus of Catholic life – God fueling us with His Pure Love (God is Love, not abstractly but actually). All of our sacraments focus around this one sacrament. It is offered at every Catholic worship service everyday of the week. It is part of every Catholic wedding and funeral (and because of this, both ceremonies are typically open to all members of the parish – you do not need an ID card.)
It is also important to remember that this belief was never challenged for over fifteen centuries. For clear proof, look at all the offshoots. The further back you go in history, the more the break away churches reflect Catholic teaching. Lutherans practice a type of eucharistic-like ceremony (though the Church teaches that it is invalid). So do the Anglicans (aka Episcopalians). And so do the orthodox churches. It is part of our constant and unbroken Sacred Tradition that goes back not just to Christ, but to the beginnings of creation itself.
If you can wrap your mind around the Eucharist, then you have the number one key for understanding everything else Catholics do: kneeling, praying to saints, confession, laying on of hands (priestly apostolic succession in an ubroken line to the original twelve apostles), the very structure of the Church.
There are those who would say Christ was only speaking in symbolic terms and there are many ways to refute this (Christ always clears up misunderstandings among His dim disciples, but lets many of them go because they were disgusted at the thought of eating His flesh.) I like to look at GodÕs symbolism: Bethlehem means Òhouse of bread.Ó When He was born, where did they put the baby Jesus? In a manger! It could not have been more clear if they had put Him on a plate! The word ÒmangerÓ means ÒeatÓ! Like when you go to an Italian restuarant, they say Òmanger manger!Ó (Okay, they donÕt, but I donÕt know how to spell the Italian … is it mange? That looks strange…)