I'd like to point out that the dialect-language-family distinction is really a continuum. As dialects drift apart from each other, there is no point where God comes in and declares a dialect has graduated into its own language. Mutual intelligibility simply decreases continuously.

For instance, Portuguese and Spanish are widely considered to be different languages, although they are partially mutually intelligible, particularly in written form. Cantonese and Mandarin are less so, but still a bit. My uncle-in-law speaks Canto but can still understand my Mandarin (however, he can't respond). I won't deny that there is a political reason to want to refer to the Chinese/中文 languages as a single "language," but the classification is honestly quite arbitrary. My understanding is that linguists generally place the category of "Chinese" somewhere between "language" and "family."

Is Scots a different language than English? I don't think I could understand someone speaking Scots without incredible concentration. (However, it's still considered a "linguistic variety" of middle english.)