I was first introduced to the concept of transubstantiation when I was a wee lad taking courses in Confraternity of Christian Doctrine (CCD). It was there were my classmates and I learned that during the sacrament of Communion, the Eucharist — or bread/holy wafer — was consecrated so as to become the "body of Christ." Not the symbolic body of Christ, but the actual body of Christ.
After eating Jesus, it is customary for adult Catholics and precocious youngsters to wash down the flesh of Jesus with ... the blood of Jesus. Yes, the sacramental wine is also blessed and miraculously transformed into what Michael Jackson called "Jesus juice."
One of the bones that Martin Luther picked with the Church was transubstantiation, which is why Protestants do not believe that tasteless wafer and diluted wine are the literal body and blood of Christ.
But why does the Catholic Church teach this doctrine? Because this is what Jesus is alleged to have said at the Last Supper:
"And as they were eating, Jesus took bread, and blessed, and brake it; and he gave to the disciples, and said, 'Take, eat; this is my body.'"
Needless to say, this was one of the issues I had with the Church as well. My priest personally insisted to me that I "had to believe" that the bread and wine were the actual body and blood of Christ, something I was unprepared to do, given the fact that the belief is so obviously false. And yet, here was this 65 year old man telling the opposite. The whole episode was ridiculous, and one of the many reasons I am no longer part of that organization.