"No, we can't cross the ocean there, don't you see that sea monster in the way?"
Aside from the fact that, as we've already explained, most people in the Middle Ages did not think the Earth was flat, the church wasn't responsible for killing science -- to the contrary, it was largely responsible for saving it.
After the barbarians invaded Europe and Rome went the way of the dinosaurs, the Catholic church was the last remaining aspect of Roman culture in Western Europe. The church went about setting up monasteries across Europe, and along with the monks came the monks' massive libraries. Monks were just about the only educated people in the early Middle Ages, and pretty much everything we know about this entire time period was written by them.
"Look, the monks' scroll clearly says that all monks had 12-inch dongs, so it must be true."
As time went on, the church stepped it up a notch and started establishing universities to foster the preservation of knowledge. You may have heard of a few of them: Oxford, Cambridge, and the University of Paris (not to mention pretty much every other top school in Europe). At these universities, students studied more than most college kids do today, with an average bachelor's degree taking up to seven years to earn, and a master's or doctorate taking several more. The universities were also big on translation, having successfully translated into Latin guys like Aristotle and Plato, which effectively made the Renaissance possible. All of this despite the fact that beer bong technology was still in its infancy.