I'm not very familiar with the Catholic church. Your saying that true Catholics believe Jesus sliced pieces of his own body to feed to people? Eating the flesh of another is cannibalism.
You've found the crux of the "cheap shot" that is often taken against the Catholic church. It is known as the doctrine of transubstantiantion. The belief is that the bread and wine becomes the literal body and blood of Christ in a mystical miracle. When I was in boarding school at a Catholic monastery I recall hearing that some naysayers were even pushing to have doctors come in and examine the host (as the Eucharistic wafer is called) after the point in the mass where the priest declares it the body and blood of Christ.