When it comes to language, I am more of a descriptivist than a prescriptivist: I would rather document how people use language than hit folks over the head with how they’re using it wrong. However…
Words do have meaning and they have history, and the first is derived from the second. Language exists primarily as a tool of communication and that communication only happens when the meanings are agreed on.
Words also have context. Sometimes that context is obscure and radically changes the intended meaning. For example, blue. We all know what blue means, right? But there’s a big difference between saying someone has blue eyes and that they themselves are blue.
Or the word terminal. If I’m a transport nerd then it means one thing (or several things depending on how finely graded your shades of meaning are for different modes of transport); if I’m a telecomms engineer it means something else. For a computer technician it means another thing again. If I’m a hospital nurse it probably has a rather more grisly, but still necessary, meaning. All of these different contextual meanings derive from the Latin “terminus” which meant* goal or end point.
So, words have meaning and context, but that context is not always clear to the listener. Whose job is it to uncover the context that illuminates the meaning?
I would say that depends. If the speaker is trying to communicate their ideas, then they need to provide the context or their ideas will be lost (this is why knowing your audience is important when writing). If the listener is trying to extract meaning from words that were not expressed without them in mind, then it is up to the listener to figure that context out – it doesn’t do any good to wilfully impose the wrong contextual meaning on a term**.
However, words do have historically-based, accepted meanings. Those baseline meanings need to be treated as the default unless context is found which changes them. I don’t agree with Humpty Dumpty, in other words: you can’t just go around making up new meanings for words willy nilly, at least not if you want to communicate anything.
Because Persian blue cats aren’t blue at all, and that’s just weird.
[*] I think the past tense is appropriate here since this refers to the Latin which formed the root of so many other languages rather than the conlang that is spoken in the Vatican.
[**] although you can construct quite a lot of jokes this way.