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My only question though would be what do we call - generically - the "Short"? Mini? Child's? Extra Small? There's not set convention on what they should be called. In your example of 8, 10, and 12 ounces you're only correct insomuch as there are only three options and objectively small, medium, and large are correct relative to the other options. You provide no options for smaller than 8 oz or larger than 12 ounces, as there are with Starbucks. You argument needs to be extended to included more than three sizes. But you can't because mini/extra small/tiny are all relatively the same per your use.
Also the point of the Paul Rudd skit mentioned is being severely misunderstood.
Small, Medium, and Large aren't just labels, they are descriptive terms.
If you have an 8 ounce, 10 ounce, and 12 ounce size those ARE small, medium and large by definition regardless of what you want to call them.
Someone ordering a small drink means they want the smallest serving you sell.  Nothing in whatever you label the drink sizes can change that.
It's like if you go to a cupcake shop and the menu behind the counter just shows a blue cupcakes and red cupcakes and you order a red cupcake and they go "I'm sorry we only have magenta and aquamarine."  Motherfucker you know what they meant.