It’s not offensive, but it’s horribly incorrect. It’s like saying people from France and Albania both speak “European”. I mean, there are a group of languages that all use the same alphabet and that’s the same thing, right?
There’s no such SPOKEN language as “Chinese”. However, there is a WRITTEN language called “Chinese” (which the Chinese call “Hanzi” after the Han dynasty) which is the oldest continuously used writing system in the world.
There is also a “Chinese language family” where they all use Hanzi to write their language.
However, the different dialects of the Chinese language family are, unlike say Spanish and Portuguese or German and Dutch, pretty much mutually unintelligible. The two major dialects are Mandarin (spoken by more people than any other as a native language) and Cantonese, although there are about a dozen others that have at least a million speakers.
The thing is that although Mandarin and Cantonese are related language, and use the same writing systems, and are often spoken in areas right next to each other, they are completely different spoken languages.
Note that for the exact same English translation, and the fact that the characters used are identical, the spoken forms have nothing in common. Cantonese has a different syllable and tone than Mandarin for the vast majority of Hanzi characters. Cantonese has more tones. It has a different rhythm. There are grammatical differences.
As such, when referring to spoken languages, use the Western term for them instead of lumping them together.