It is known that all neutrinos are lefthanded (for simplicity I don't discriminate between the technicalities of handedness and helicity), though in the answers of this question one can read that the major part of the neutrinos is non-relativistic, for various reasons, and that they are extremely hard to observe.
Can it be that also all electrons, at the moment they came into existence after the big bang, had the same handedness?
Because neutrinos haven't interacted with other matter since their creation after the big bang they preserved their left-handedness (neutrinos in the cosmic neutrino background, are supposed to be non-relativistic and to constitute the major part of the neutrinos, which is very hard to prove though).
Electrons, on the other hand, have electromagnetically interacted a lot with other electrically charged matter, so over time, they developed right- and lefthanded ones in equal amounts. In the same way, the non-relativistic neutrinos should also have developed right- and lefthanded ones in equal amounts, but this is, as I wrote, very hard to verify because of the very tiny masses of non-relativistic neutrinos. Only the (relativistic) neutrinos in standard experiments reveal that the neutrinos come exclusively in left-handed versions.
This implies of course, that the electrons had a velocity near the speed of light when they were created after the bang, just like the neutrinos. This is the case in different scenarios. I'm inclined to bring on the Rishon Model to discuss one of these scenarios but I can better refrain from doing so because it's pretty much non-mainstream, so I rather stick to the mainstream hypothesis that before the electroweak symmetry broke the electrons (and neutrinos) had no mass.
If the answer to this question is yes then the electron and electron-neutrino (and the muon and muon-neutrino, and the tau and tau-neutrino) are on a more equal footing or more symmetric with respect to each other (apart from the electric charge of the electron) than thought (and again I'm inclined to...).
I'm inclined to bring on the Rishon Model, but I can better refrain from doing so because it's pretty much non-mainstream.