The hint from quantum field theory (and things like lattice gauge theory) is that charge emerges from interesting topological states/defects of the underlying field (by "interesting topological shapes" I mean - imagine a vortex in the shape of a ring/doughnut). It's kind of a topological property of a state of the photonic field, if you will - something like a winding number (which has to be an integer). Electric charge is a kind of "defect" or "kink" in the photonic field, while color charge (quarks) are defects in the strong-force field, etc.

When an electron-positron pair is formed from a vacuum, we get all sorts of interesting geometry which I struggle to grasp or picture clearly. I understand the fact that these are fermions with spin-1/2 can similarly be explained as localized defects in a field of particles with integer spin (possibly a feature of the exact same "defect" as the charge itself, in the photonic field, which is what defines an electron as an electron).

EDIT:

> However, there are no theories why this is -- they are simply measured and that is it.

My take is that there _are_ accepted hypotheses for this, but solving the equations (of e.g. the standard model, in full 3D space) to a precision suitable to compare to experimental data is currently entirely impractical (at least for some things like absolute masses - though I think there are predictions of ratios etc that work out between theory and measurement - sorry not a specialist in high-energy physics, had more exposure to low-energy quantum topological defects).