These days, neutrinos are left-handed, just as they were a long time ago. These days electrons are right- as well as left-handed. Were they only left-handed a long time ago, before having interacted with any force field?
I can imagine that neutrinos still are left-handed today as they barely reacted with matter. Electrons have reacted though, and maybe they have developed a right-handed portion well as a left-handed portion. They don't move at lightspeed anymore (so at lightspeed after just after creation).
Before the Higgs field became effective, all particles moved at the speed of light. Wouldn't the theory be more symmetric if besides left-handed neutrinos, also one-chirality electrons were created? Or is a theory with two chiralities from the start more symmetric (for both the electron and the neutrino)?