Why Dirac wanted to create the Dirac equation and solve it? Because he wants an equation that describes matter in a world where:

• Probability is conserved
• Spacetime is Lorentzian (special relativity is non-negotiable)
• States superpose (quantum mechanics)
• Time evolution is causal and first-order

Special Relativity wants $E^2 = p^2 + m^2$ and Quantum mechanics wants linear time evolution. Given it has to transform under Lorentz transformations; carry intrinsic angular momentum (spin) and admit a conserved current, so the object cannot live in spacetime itself — it must live in a representation space of the Lorentz group. Put in another way, matter is a section of a spinor bundle over spacetime.

Caveat, given space time “distance” t2-x2 does not have to be positive or 0,