Can I Just Get A Small, Please?

This is a conversation I just had with a waitress at a fast-food joint:

Me: … and a small Coke, please.
Fast-food waitress: We only have medium and large.
Me: Y’all must’ve sold a lot of smalls today.
FFW: No, we don’t sell a small size.
Me: <smiling> Then you can’t have a “medium” if you don’t sell a small.
FFW: <weird stare>
Me: “Medium” derives from the Latin word “medius,” which means “middle.” In order to have a “medium,” you have to have something both larger and smaller.
FFW: <weird stare continues>
FFW: <weird stare continues>
FFW: <weird stare continues>
FFW: So, you want a medium?
Me: <sigh> Yeah, I’ll take a medium.

As best as I can figure, this is about the sixth time I’ve participated in some version of this back and forth. Not once has my interlocutor understood what I was saying.

English and basic reasoning have been losing for so long. Sad!