> Even the "why does matrix multiplication look that way" is incredibly deep but practically impossible to motivate from other considerations.

Short, simple answer to that question by Michael Penn: https://www.youtube.com/watch?v=cc1ivDlZ71U

Another interesting treatment by Math the World: https://www.youtube.com/watch?v=1_2WXH4ar5Q&t=4s

There's no impenetrable mystery here. Probably just bad teaching you experienced.