linguistics1-9  Exercise 2: Language or Dialect?
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Intelligibility fails as the only test, because:

  - Danish and Norwegian are largely mutually intelligible, yet they count as
    two languages: each has its own standard, written form, literature and
    national identity.
  - Mandarin and Cantonese are not mutually intelligible when spoken, yet
    they are called dialects of Chinese: they share one writing system and
    one national and cultural identity.
  - Intelligibility is also a matter of degree (it varies by speaker,
    exposure and goodwill) and often works in a chain: neighbouring dialects
    understand each other, while the two ends of the chain do not.

What else decides it: politics (nations and borders), the existence of a
separate standard and written form, history, and how the speakers see
themselves. The saying "a language is a dialect with an army and a navy"
makes the same point.