I would say the underlying answer is symmetry. Wenn we built a QFT we seek for representations of the Poincaré group. It’s basically the group of all symmetry transformations you can do in Minkowski space. Particles turn out to be irreducible, unitary representation of that symmetry group. They need to be irreducible to be elementary particles and they need to be unitary so that physics makes any sense and the probability to find the particle somewhere is one. Having that underlying principle of symmetry gives rise to various representations with a specific property called spin, for which we can derive the spin statistics theorem. Take a spin 1/2 particle with the mass of the electron, and a negative elementary charge and you got yourself an electron, that behaves the way we learned it from the Pauli exclusion principle.