Slippery cup + wet hand = dropped beverage.
So, cups have this design so that as gravity pulls the drink downward, the flaring taper counteracts that effect keeping it safely in place inside your hand.
If the taper went the other direction, as you squeezed your hand tighter, you could actually force the cup through your closing fist (kind of like squeezing a slippery bar of soap and it popping out of your hand.
Also, it’s WAY easier to store 100 cups if they all fit inside each other, than if they have to be individually placed on the counter. Uniform width, and fat bottomed cups can’t stack inside each other.
Edit: Typo
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