Our physical intuitions are Galilean, not classical, mechanics (that is, they are non-Newtonian). For example, our intuitions tell us that an object set in motion eventually slows down and stops. That's Galilean (also termed "folk physics" or "naive physics", usually by cognitive scientists).
Most of us had to study formal physics to advance to Newtonian classical mechanics.
Quantum mechanics (QM) is completely non-intuitive, at least as far as intuition about either folk physics or Newtonian classical physics is concerned. IIRC Feynmann says as much in his book "QED: The Strange Theory of Light and Matter", Chapter 28 beginning:
"I think I can safely say that nobody understands quantum mechanics. —Richard Feynman
The quantum theory is not explicable in commonsense terms..."
Of course Feynman used his real-world physical intuition all the way through to his most abstract work. In one case he characterised the internal structure of the proton as being like "marbles inside a tin can." Try and write those equations!
