In the Standard Model properties are defined as relationships within/between symmetry groups. There are only so many things you can do to/with/in a symmetry group, and that's where the quantisation comes from.

But... that's a mathematical metaphor applied to observations. It's a good fit, but it doesn't explain why it's those symmetry groups and not others, or why symmetry groups are a good fit at all.

There's likely some kind of fundamental mechanism that generates these symmetries, and no one knows what that is.