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I'm going to copy-paste the exact relevant bit here:
I knew about the chirality difference, that there are no right-handed neutrinos nor left-handed antineutrinos (or something along those lines, breaking what was thought to be a fundamental parity or symmetry), but what puzzled me was that I thought the charge difference was the one big fundamental difference between matter and antimatter, and suddenly tonight the neutrino question popped into my head. At the very least I knew that it's not a mass/negative mass type of difference.
Now as for that bit that says "opposite signs of lepton number"... I'd never even heard of this concept or characteristic, until right now.
Lepton number is an observationally conserved quantity. As far as I know there’s no fundamental reason for it to be conserved (and indeed there are searches for physics beyond the standard model that would violate it) but it’s been found to generally be conserved in reactions so far. Lepton particles have a lepton number of +1, lepton antiparticles have -1.
There’s a similar conserved quantity known as the baryon number, with a similar definition. Protons and neutrons (baryons) have values of +1, anti-protons and anti-neutrons are -1.
An example: consider the beta- decay of a neutron, baryon number +1 and lepton number 0. It emits a proton (baryon number +1), an electron (lepton +1), and an electron anti-neutrino (lepton -1). Total lepton number of the decay products is 1-1=0, so the value is conserved.