Physicists soon came up with a way to make the laws look better again. While it was found that only left-handed neutrinos exist in nature, it was also found that only right-handed antineutrinos exist. This meant that while a parity exchange on its own does not always produce the right equations, applying a parity exchange and swapping all particles for their antiparticles should work. Physicists call the process of switching particle for antiparticle charge conjugation. They discovered that their equations were symmetric under a combined parity exchange (P) and charge conjugation (C) - they were CP invariant.
All this means is that if you take the equation of motion for a neutrino and switch +x for -x the resulting equation does not correctly describe a neutrino. However, if you then switch neutrino for antineutrino the equation works again.
Everything seemed to work very well, until 1964....