Hello Infinity.
I'm a mere English learner from Japan, but could you allow me to throw my 2 cents on your question?
Frankly speaking, I'd say you'd better give up the hope you could get a conclusive answer to the question. I have raised a similar question before in this forum but I could not get enough persuasive responses (
Post:56071).
As for some nouns (especially substantive nouns), English distinction between countable/uncountable seems mostly reasonable cross-linguistically. But for some nouns (above all abstract nouns), the distinction cannot be logically understood to non-native English speakers. I think we should take this kind of distinction as a matter belonging to the realm of linguistic habit particular to English rather than to the realm of universally available reasons. Countableness for some nouns is different even between similar European languages. For example, "information" is deemed as uncountable in English but it is countable in French and German. So I think we had better learn English's countableness of nouns without asking why it is so. (
BBC grammar QA).
Nevertheless, I'd like to add about your question what I feel personally. I think English people someway has a tendency to take a thing as countable in the case they could feel there would be things similar to that thing. For example, let me take the case of "knowledge". When you say "knowledge" without adding the indefinite article "a", it means a general and indefinable amount/sort of "acquaintance with something through experience and intelligence". But when you say "He has a knowledge of biology", the noun phrase "a knowledge of biology" is interpreted to imply "a certain sort/amount of knowledge on biology such as that you can imagine other people also might have one similar to that. It is my humble opinion.
Anyway as I'm a beginner of English learning and don't know much about English, you'd better not believe me so much. Our teachers and other native speakers must give you much much better answers. Please wait until then.
paco