It's the opposite: "it's a different language" is usually just a nationalistic desire for differentiation of what are essentially dialects/variants of a language.
>Linguistically, it does not matter -- there is no objective definition of the difference between a language, a dialect, or whatever -lect.
That's more because academic linguistics, as developed in the latter half of the 20th century, had to pay lip service into several ideologies, rather than there not actually being good practical ways to discern e.g. arabic as a single basic language with different variants.