Matter of fact, what do we do with our neutrinos now? Are they defined as matter, anti-matter, or do we just leave them in the "ill-defined" basket for the time being?
We have observed no right-helicity neutrinos thus far. This means that neutrinos may be majorana particles (which is a fancy way of saying a neutrino is its own anti-particle).
In a similar vein, why is it that while quarks and leptons both have two main "families", the quarks are split into positively-charged and negatively-charged families, but the leptons are split into negative and neutral?
There is no obvious reason things have the charges they do, but proponents of grand unified theories say its because everything fits into a larger theory.
Just like the current "quark" is actually a field with three component "colors," some have suggested you can put several components of the standard model together as fewer fields with different symmetries. You can fit the standard model's many fields into two components in an SU(5) symmetry group (the 5 dimensional and 10 dimensional representations).
Even more elegant- the entire standard model fits perfectly into the 16 dimensional representation of the SO(10) symmetry group, with room left over for a right-helicity sterile neutrino.