Ah poisson brackets!
I think what you are looking for is Noethers theorem.
Susskinds classical mechanics course on youtube, i think lecture 4 (symmetries) and 8 (poisson) will help you.
Considering the amount of answers, the question: Why is quantum so difficult, seems pretty difficult itself.
If one focuses on teaching of qf, the idea that one should or should not start with the old quantum theory is not so evident.
In 1992 Fischler & Lichtfelt...
Lets say a state is defined by the minimal amount of independent variables to completely describe a system.
One would come up with the (q,p)-phase-space for a point mass and as another example the Hilbert-space for quantum-states.
Consider the very simple case of a standing wave in string...
Perhaps start with some history to see te need for the theory? The most simple but basic: Polkinghorne: quantum theory, a very short introduction (5 Hours read if you're into some physics)
Gary Bowman: Essential quantum mechanics. Starts you off with the postulates and learns you formalism and...