I'll take a shot at this. The "answer," such as it is, is symmetry. The electron belongs to a group called the leptons, which is to say they are lightweight. Leptons obey certain sorts of statistics and consist of the electron, the muon, the tau lepton, the electron neutrino, the muon neutrino, the tau neutrino, and their antiparticles. That's twelve in total.
The mirror of the leptons would be quarks. Up, down, charm, beauty, top, and bottom ... and their antiparticles. Twelve again! Their charges are 2/3e, -1/3e, 2/3e, -1/3e, 2/3e, -1/3e, and the reverse for the antiquarks. One bundle of three quarks is the proton, and it happens to be 2/3e + 2/3e + -1/3e. But so what? There's all kinds of other bundles. Three-quark bundles are typically hadrons (heavyweight) and two-quark bundles are mesons (medium weight). So you have a lot of choices on the other side!
The choices are caused by something called color confinement, which states that you will not get quarks alone. Indeed, you can take a pair of quarks in the aforementioned meson, and if you stretched them further and further apart, when the bond between them (mediated by gluons) snapped, you would have put so much energy into the stretching and snapping to create two new quarks, one at each end of your broken rubber band. Just as you cannot cut a piece of string such that it only has one end, so you have it with color confinement. I don't want to get too far away from the main point but because of this, quarks are found (normally, outside of Big-Bang quark-gluon plasmas) in combination ... and so eventually one of the combinations has a charge number resembling that of the electron.
Also, positrons aren't really the opposite of electrons. They're opposite on the matter/antimatter axis, which automatically flips the charge, q. They are not opposite along the lepton-quark axis, nor are they opposite along the electron-neutrino axis. Instead of one mirror, imagine many mirrors at angles to one another, and "opposite" becomes a less useful term.
One problem with your explanation is that the muon and the tau (and the pion as a decay product of the tau) all decay into electrons, neutrinos and photons, which would suggest that neither muon or tau are fundamental.
This would put the fundamental leptons being only the electron (and its antiparticle) with the neutrino and the photon.
I never suggested that they are fundamental, and nobody said that the symmetry is perfect. In fact, the way the various symmetries break is what gives rise to all of this complexity and only raise more questions.
Also, photons are not leptons -- wrong spin for that. Which in turn can raise yet another axis for our funhouse of mirrors: fermions versus bosons.
The mirror of the leptons would be quarks. Up, down, charm, beauty, top, and bottom ... and their antiparticles. Twelve again! Their charges are 2/3e, -1/3e, 2/3e, -1/3e, 2/3e, -1/3e, and the reverse for the antiquarks. One bundle of three quarks is the proton, and it happens to be 2/3e + 2/3e + -1/3e. But so what? There's all kinds of other bundles. Three-quark bundles are typically hadrons (heavyweight) and two-quark bundles are mesons (medium weight). So you have a lot of choices on the other side!
The choices are caused by something called color confinement, which states that you will not get quarks alone. Indeed, you can take a pair of quarks in the aforementioned meson, and if you stretched them further and further apart, when the bond between them (mediated by gluons) snapped, you would have put so much energy into the stretching and snapping to create two new quarks, one at each end of your broken rubber band. Just as you cannot cut a piece of string such that it only has one end, so you have it with color confinement. I don't want to get too far away from the main point but because of this, quarks are found (normally, outside of Big-Bang quark-gluon plasmas) in combination ... and so eventually one of the combinations has a charge number resembling that of the electron.
Also, positrons aren't really the opposite of electrons. They're opposite on the matter/antimatter axis, which automatically flips the charge, q. They are not opposite along the lepton-quark axis, nor are they opposite along the electron-neutrino axis. Instead of one mirror, imagine many mirrors at angles to one another, and "opposite" becomes a less useful term.