I remember seeing two main camps in the old debate on whether a hot-dog is a sandwich: those that argued "it's meat between two pieces of bread, therefore it's a sandwich" and those that counterargued "if I asked whether you wanted a sandwich and then gave you a hot-dog, you would be surprised". And both sides are right! That said, one of them is more right from a language-theoretical point of view, and that's the point of today's post.
(Spoiler: the "not a sandwich" camp is right. Sorry, pro-sandwichers!)
According to Herbert Clark a dialogue is a cooperative activity. It is a joint activity in which both speakers try to accomplish a common objective, ranging from something as formal as "make me understand where the train station is" to as vague an objective as "let's kill some time". And because it is cooperative, we do not expect the other person to be deliberately obtuse. If I ask "Can I get you something to drink?" and someone replies "I don't know, can you?", nobody would assume that this person has a genuine interest in my capacity for carrying drinks. Instead, we would immediately see this for what it is: that this person is not cooperating, that any reasonable person would have understood what I meant, and that this person stopped cooperating on purpose. Whether he did it to make a joke or because he's a jerk, that's a topic for a future discussion.
There is also a principle called the "maxim of quantity" (one of Grice's four maxims) according to which a person will always give as much information as possible, but not so much that it breaks the dialogue. If someone asks me where I come from, my answer can be as precise as a specific neighborhood or as vague as "somewhere near the border with Brazil". My answer will depend on how familiar I believe the other person to be with South-American geography, because I don't want to give them excessive information that they cannot handle. Again, I'm cooperating.
Which brings us to the hot-dog debate. From a taxonomic point of view, a hot-dog is a sandwich: it is composed of two pieces of processed meat between two pieces of bread, which is as clear as it gets. But this is only half the story.
The definition of sandwich came long after the sandwich itself. It is an artificial construct designed to model and understand a set of real-life language usages. Spoken language, on the other hand, is the real deal. Language rules and word definitions model how we speak, and not the other way around. All definitions are artificial and, therefore, may not always reflect the way we actually use those words.
Bringing this all together, I would only use the word "sandwich" to describe a hot-dog if I had a reason to believe the other person doesn't know what a hot-dog is. If you know what a hot-dog is and I know you know what a hot-dog is, using the word "sandwich" to speak about a hot-dog is neither maximally informative (I am giving you less information than I could) nor cooperative (I know which word would help us the most, but I'm not using it). "Sandwich" is a catch-all word that can only be used when no better word exists.
Even worse: you know we both know what a hot-dog is. By choosing "sandwich", I am actively leading you to believe that I want to offer something that can be described as a "sandwich" but not as a "hot-dog". Fans of malicious compliance will argue that this is not technically untrue, but you and I both know that there's little practical difference between "I told you a lie" and "I told you something that any sane person in the world would understand in a certain way while secretly using a different, opposite interpretation that I kept to myself".
So there you have it. A hot-dog is a sandwich if you stick to rigid categories created by researchers with a tenuous grasp of the real world at best (you know, people like me), but you are only allowed to use it if you talk to people who never heard about hot-dogs before. Using the word "sandwich" for a hot-dog in any other context is uncooperative, mildly dishonest, and kind of a jerk move. People do not use the word "sandwich" like that and, since spoken language is where "true" language usage lies, they are the ones who are using it right.