It's all about chucking it fast, and getting it in place for the flip. So down fast, in place for the flip. Some people do one-handed play, which means you can't touch it with one hand, using the other to do everything. You want to drop a beer, put it down, and be ready to flip that cup immediately, because that's what's going to get you onto the next game. And you want it there so quickly, because if you do mess up, you want to be able to get it right back and have enough time before your opponent finishes drinking their beer to try to flip it again and move it on to the next person.
It's just a matter of efficiency, getting rid of the beer and getting your cup in place to be flipped as quickly as you can. Then there's another aspect: cheer on your team, you can never get down. If someone is messing up their flip, the thing that's going to make them mess up worse is getting negative on them. That will make them doing even worse. "Come on, this is you! Put it up there! This time!" Try saying things like this instead. All positive. That's what gets the game won.