a language is as much a political, cultural and historical notion as it is a purely linguistic notion
It's even more clear here that Cantonese is definitely beyond simply a dialect. In a cultural way, Cantonese has developed its own cultural impact to the society such as Cantonese songs and Cantonese movies, TVBs, and etc. With culture involved, Cantonese cannot be as simple as a dialect
. It is widely known that Mandarin speakers and Cantonese speakers do not understand each other
Not just the difference between Mandarin and Cantonese, there are many dialect speakers in China that could not understand each other. The grammar, pronunciation, syntax and many other aspects of these dialects are mainly different.
Mandarin and Cantonese are not mutually intelligible but there are different academic opinions whether Cantonese is an independent language.
In a linguistics class I studied last semester, it said that there's an easy way to distinguish a dialect and language. If you can understand it, it's a dialect, but if not, it's a language. So technically, there are many dialects in China should be considered as languages in linguistic way, but it's just because of political reasons that we have to call them dialects.