Unironically, magnetism is similar to charge, which is similar to mass.
You (probably) wouldn't ask "But why does an atom weigh anything?" or "why do opposite charges attract?" All these things are just intrinsic properties of matter: they just have them.
So the answer to questions regarding why anything has mass/charge/magnetic moment really come down to "they just do."
Now, if you want to talk about how and why magnets work at a macroscopic scale, we can have a long and interesting chat about long range ordering and phase transitions, but I'll leave that for now :)
There's a lot more to it than "they just do" we just don't know yet because there's actually a lot we don't understand about the fundamental properties of, well, fundamental particles.
See the higgs boson as for why matter has mass. We used to say "inertia is a property of matter" but some clever fucks figured out why and then proved it.
Mass & gravity are still way easier to understand on a fundamental level, especially since everything has a certain amount of mass and thus affects and is affected by gravity. It's a much simpler concept.
("Natural") magnetism is (so far) very material specific and I don't think I've seen a good explanation as to why exactly. Magnets certainly behave very differently than other materials and that causes this mysticism in people when they think about magnets. Given the still ongoing research into magnetism and related things like superconductivity there's certainly a lot still to learn.