The core of your question seems to be about how subordinating and coordinating conjunctions work with dependent and independent clauses. Here's my take in a nutshell.
A subordinating conjunction is part of the dependent clause, and we can prove this by rearranging a sentence: an experienced speaker will intuitively move the conjunction together with the clause. Here's an example:
- We left the party because the house caught fire.
- Because the house caught fire, we left the party.
Shifting from observations about structure to observations about meaning, we can see that the logic of the sentence changes if we put the subordinator in the wrong phrase: "The house caught fire because we left the party" is not the same as the earlier statements.
The classic coordinators (and, but, or, and nor – which is 'or' negated) don't work this way. These two sentences are basically equivalent:
- We left the party and the house caught fire.
- The house caught fire and we left the party.
True, a listener might make inferences about time and logic because of the order of the clauses, but the sentence does not necessarily express any implication of time, consequence, or causation through "and," and many grammarians will say that "and" is not part of either clause.
SO: bearing in mind that grammar is a contested field, let's take on the FANBOYS treatment.
Where things get sticky is with for, yet, and so. 'Yet' and 'so' are old adverbs that work as conjunctions, and 'for' is an old preposition that works as a conjunction – and there are some fuzzy boundaries between prepositions and adverbs, so we should expect complications.
The most important reason some people say they are not coordinating conjunctions is that, unlike 'and', 'but', and 'or'/'nor', they are clearly part of a clause. We can't reverse clauses around them and preserve the same meaning; we can show that 'for' works a lot like 'because' with this example:
- We ate, for the food was hot.
is not synonymous with
- The food was hot, for we ate.
However, in MODERN English, we can't acceptably relocate the 'for' phrase to the beginning of the sentence:
- *For the food was hot, we ate.
We see that these three words don't act like prototypical subordinators, either, which is the reason some people think of them (and class them) together with the coordinators.
There are other differences, too: 'for', 'yet', and 'so' don't work in the same variety of settings as 'and', 'but', and 'or'/'nor' do; the latter can fit into all kinds of phrases. Also, 'yet' and 'so' still work as ordinary adverbs, and 'for' works as an ordinary preposition, which adds the to the confusion.
Basically, I don't consider 'fanboys' a useful categorisation for discussing syntax, even if it provides a rule of thumb for comma placement. I'm also against being snarky about the issue, because it's genuinely confusing, and grandstanding about grammar is for people who sneer and ask little kids "I don't know, CAN you go to the bathroom?" You know who you are. Repent and do better.
