>Shanghainese is called a Chinese dialect, but it is a Wu language. It is not a dialect of Mandarin (aka the Beijing dialect), but it certainly is a dialect of a common "Chinese" language, even though it is a descendent of a language family that is not most closely related to Mandarin.

That's the problem isn't it? A language is assumed to be a dialect of another language just because it uses the same script, regardless of its origins or how mutually intelligible it is. Reminds me of how Russian nationalists don't consider Ukrainian or Belarussian separate languages, but dialects of Russian just because they're written in Cyrillic. Might as well say that English, Hungarian and Vietnamese are dialects of Latin, just because they all use Latin script.

Same with Lisps really. People see the parentheses and assume all of these languages must be very similar, even though they really aren't.