It’s all strange, yet true – quantum theory is the most accurate scientific theory ever tested and its mathematics is perfectly suited to the weirdness of the atomic world.
It's strange when we find the unknown for the first. But it is strange when we can not repeat or explain it. By increasing our interest, we become acquainted with strangeness, and it becomes familiar and familiar and controlled. When a novelty learns well enough, then everything happens exactly as in quantum theory.
Echoing what Emil has said, all the predictions made by quantum theory, even the strangest and most unintuitive of predictions seem to be realised in nature. Because of this, just about everyone believes that Nature is inherently quantum.
Classical mechanics is ideal for a macroscopic world. Hydrodynamics is perfect for fluids. Quantum mechanics is OK for the world of atoms. Classical electrodynamics describes the behaviour of a charge and photons. A submicroscopic concept is able to describe the world starting from Planck's scale (and it allows the derivation of the formalism of quantum mechanics at the atom scale).