They share the majority of the syntactic and grammar. Their written form are all the same. Pronunciation is the major difference. This level of unity is established probably since the Qin dynasty.
Easiest way to see this difference is watch the news in Cantonese -- it is mostly 书面语 (standard) mandarin but pronounced as Cantonese, whereas day-to-day spoken Cantonese is completely different in structure and vocabulary. What do you think gets written in HK movie scripts? Definitely not standard written mandarin.
Your assertion is a political one, and not universally shared. The Central Party has incentives to make that claim for nationalist reasons, and has been doing so for decades, but that does not necessarily make it true. In my personal opinion, whether it is a dialect or not should be answered by the people who speak it, not by the people who rule them.
Well, you sort of prove my point, that it's a political thing, about the unity of the country.
Here's what linguists say:
1. From "Visible Speech: The Diverse Oneness of Writing Systems" by John DeFrancis:
"Chinese [...] is an umbrella designation for at least eight present-day varieties of what are usually called "dialects" but, since they are mutually unintelligible, might better be considered parallel to the various languages that make up the Romance group of languages."
2. From "Asia's Orthographic Dilemma" by Wm. C. Hannas:
"some eighty million or more people living in China [...] speak non-Chinese languages written in alphabetic or indigenous systems. [...] If we ignore this inconvenient phenomenon and focus on the speech of China's Han population, we find a collection of at least seven or eight mutually unintelligible varieties that in any other context would be called "languages," but which are "dialects" in China, in part for political reasons and in part because of a problem with the translation of the Chinese term fāngyán. The political motivation for claiming that these distinct varieties constitute a single language is fairly obvious: it is easier to govern a country in which the majority believe they are speaking one "language" (whatever the linguistic reality) composed of several "dialects" instead of several related languages.
[...]
Most linguists familiar with the classification problem acknowledge that the major Chinese varieties differ from each other at least on the order of the different languages of the Romance family.
[..]
We have seen that the Chinese languages differ not just in pronunciation but also in vocabulary and grammar, and that these differences are realized through unique morphemes (or unique uses of shared morphemes) for which characters do not exist at all, do not exist in Mandarin, or are used with different meanings and functions. Consequently, character texts in Cantonese and (where available) in Taiwanese are largely unintelligible to Mandarin readers. Many characters are completely unfamiliar; others are recognizable but make no sense in context. This occurs where conventions exist for writing the non-Mandarin variety in characters. Actually, most of these languages have no established writing system and hence lack even the possibility of being understood by readers of other varieties.
This is also true of Spanish and Portuguese but they are still considered different languages. If two people speaking different dailects couldn't understand each other they are surely different languages
To take a different perspective, calling them separate languages helps reinforce a nationalist agenda. It gives your citizenry another reason to feel separate from, and maybe superior to, other nations. Calling Spanish and Portuguese separate languages, instead of two Iberian dialects of modern Latin, helps reinforce the idea that Spain and Portugal are separate nations, and not just different regions of the same peninsula.
It's not really by default, more like by necessity. Almost all categorization schemes for human cultural artifacts are necessarily blurry at the edges, and just because someone has provided a definition that is useful for one purpose (the study of linguistic differences across cultures) does not mean that it is suited for another purpose (rhetorically implying solidarity or separation between two sets of people).
To be consistent with the linguistic facts, one should speak of the Chinese languages. You could also consistently speak of a Chinese language with dialects, and then also consider Romanian, French, Spanish, Portuguese different dialects of the Romance language; but that would redefine the terms from how they're currently commonly understood.
They share the majority of the syntactic and grammar. Their written form are all the same. Pronunciation is the major difference. This level of unity is established probably since the Qin dynasty.