"Flick the Tomato"
The best casting motion involves a gradual, controlled acceleration to an abrupt stop. Imagine it this way: If you have a tomato stuck on the end of a stick, and you want to fling that tomato into a bucket, say, 20 feet away, how do you do it? If you "whip" the stick, you end up covered in ketchup. But if you gradually fling the tomato off the stick, you might get it there. Same deal and same feel with the fly cast.