I hardly know enough about linguistics to understand your reply, but i appreciate it nonetheless.
I have some background in math; no doubt that is why I am attracted to formal linguistics. I find the diagrams linguists and computer scientists draw more convincing than what I was taught in junior high school about how to "diagram" a sentence.
In fact, most of the public school curriculum in English grammar struck me as useless. The prescribed usage of "shall" vs. "will" was just plain wrong. Any exceptions to the rules were dismissed as "Idioms". When I pointed out that there were whole families of such "idioms", I was considered a troublemaker. The word "ago" is like a preposition, but it comes AFTER its object. This observation also was taboo, since the parts of speech presented to us did not include postpositionals. Particles were mistaken for adverbs for the same reason. Even though half of the verbs in colloquial speech are phrasal verbs, this topic was never mentioned.
I have taken quite a few English classes in my lifetime, but only one linguistics class, which was supposed to be on English syntax, although we spent a lot of time on the syntax of other languages, most of which were not even Indo-European. Of course, I had not taken the prerequisites for this class. I wanted to skip the elementary survey course and jump right into something interesting.
I find it interesting that linguistics grew out of English, as psychology grew out of philosophy, statistics out of math, etc. Computer science is unusual in that it grew out of math at some schools and out of engineering at other schools.
Computer scientists draw tree-like diagrams to parse statements in "languages" such as fortran, just as linguists do for natural languages. Syntax can be ambiguous, i.e., there can be more than one tree that fits a sentence, or even a single word (e.g., "unbuttonable"
. This phenomenon is verboten in computer science but unavoidable in linguistics. That's because natural languages are messy and don't fit any set of rules very well. (I think you pointed that out already.)