the level of neurosis you are displaying here indicates that you have the potential to be a BRILLIANT musician...lol.
I suspect similar.
I can't get my head around why Pi is infinite...
You don't need to know why Pi is infinite in order to use Pi.
Example: If all you need is area of a circle πr
2 is all you need to know. Trying to understand the why and how of Pi goes beyond the scope of your original problem, and only complicates matters. Of course you can make inquiry into Pi but that is a whole different stage of research - you don't need that level of understanding if your goal is to only solve a simple area problem.
Math is about making our lives easier. It is about taking tasks that would otherwise be wordy, tedious, and laborious, and packaging them up into neat and tidy concepts that are much easier to deal with and manipulate.
This leads us to music theory, which does a similar thing. It allows us to describe tendencies in real music using terminology and concepts that make it easier to think and converse with others about what is going on.
Example: You could say: there is an ascending step-wise line of eight pitches starting on E, following that F#, after that, G#, then A, then B, C#, D# and ending on E. The prevailing semitone pattern of the sequence follows: tone, tone, semitone, tone, tone, tone, semitone. Or you could simply say E major scale. The former is a mouthful to say, yet has components that lead to the understanding of the construction of scales. If you wanted to ask a fellow musician to play the said pattern of notes, which description would you deem more judicious? Conversations sure could get awkward if we didn't have established theoretical terminology.
The problem with a lot of academically taught subjects, is that academic rigor takes precedence over all other things. Often the topic itself gets lost in the dogma. I've found many textbooks have been written for an audience of peers, as opposed to an audience of first-timers to the subject. Unfortunately, many students latch on to this and end up with the perception that music theory is about mind-numbing brain twisting exercises that seem to have nothing to do with the music they are playing. It may be a case of being taught how to construct a space shuttle before one has learned to drive a car.
to illustrate this point I will teach a student a piece by ear or rote first and when they have mastered it--they think it's something I just made up--I will put the music in front of them without telling them it's the same piece. The reaction is UNIVERSAL
"WHAT!! I can't play THAT!!!"
then I smile at them and say "yes you can and you already have."
The example given by dcstudtio: illustrates how one can learn by means of understanding the big picture first, then gradually refining one's skills and abilities in layers.
When reading theory texts, have a goal in mind. Pure research for the sake of digging deeper and deeper is fun an all, but you need to keep a perspective. What is the point where it is enough to carry out the musical task. Do you need to know the development of temperament systems and what has led to our current use of equal temperament in order to practice your E major scale? No, but it is a fascinating subject if you choose to dig in, but you don't have to.