It seems odd to me. After all, can't you learn just about everything about the human body with just one corpse? Have a whole classroom attending and the lesson is learned.... right? Nor would I expect these cadavers to be in short supply. Surely there were plenty of old, sick or murdered people with no family on which you could perform your slicing ways?
There's a few core reasons. The first is that whenever you cut into a body to explore you're destroying something. Often the basics of anatomisation (the term the English used) allowed one to take out the major organs fairly easily, but if you were studying blood vessels or nerves it sometimes required a different approach.
The second, and far more important reason is that dissections were performed for study and teaching. Students would watch a learned surgeon cut open a body and study the organs, then at some point they'd need to do it themselves. The number of bodies required wasn't immense, but there was a steady demand.