Cantonese and Mandarin intelligibility?

Cantonese is more closer to the ancient northern chinese language. Mandarin is a sinitic language which is mixed with Mongolian and Manchurian languages. The main difference between the two languages is the pronunciation of words. I would say they are like Spanish and French.

Cantonese preserves many sounds of the ancient chinese language which Mandarin Chinese had lost. This is why Cantonese language sounds strange and incomprehensible to Mandarin speakers but the sounds of the Cantonese, are actually the sounds of the Tang Dynasty's northern language. The transition from Middle Chinese to modern Mandarin Chinese is the loss of sounds.

They're separate languages. But because Cantonese and Mandarin belong to the same language family ("Sinitic") but are quite different, they're a bit like, say, Icelandic and English.

Unfortunately, however, Cantonese and all the other Sinitic languages other than Mandarin are in decline because the written "Chinese" taught now is basically Mandarin -- though perhaps with other pronunciations.

There is no intelligibility between the spoken languages. One is a "dialect" of the other only because of the political superiority of the Chinese government and the cultural influence of mainland China.

If you listen closely, there are similar words and "borrowings" between the two languages, but they are no more alike than English and French.

The implication that the two "dialects" are fully separate language implies equally separate history, ancestry, and culture, which doesn't fit in with the unified agenda of the Chinese power structure. One world, one dream, one language, one ideology. That's the party line, and few dare stray from it.

Chinese and Cantonese are two languages like English and French

A better analogy might be two languages like Portugese and Romanian. They both can from Late Latin, but only the odd word would be mutually intelligible.