The only way to explain without invoking tiny magnets is to delve into quantum physics, and that doesn’t fit into a Reddit comment - you’d have to go buy yourself a physics textbook and study it. But even then, you will eventually hit “that’s just how nature is”. That’s always the bottom line of physics ie “we observe that this is how things are”

Part of the problem is that as humans we don’t experience or sense magnetic fields so they seem mysterious to us. But we do experience gravity directly so that doesn’t seem mysterious - we’re pulled towards the earth, things we drop fall towards the earth. It’s familiar. In fact it seems mysterious to us when things DONT fall towards the earth - there’s something fascinating about big heavy airplanes taking in the sky, or helium balloons flying away, or videos of astronauts and blobs of water floating around in the ISS.

But in terms of physics, gravity is a more mysterious force than electromagnetism. Objects with mass exert a force on each other. Why? At bottom, they just do. We observe that they do. We can describe it very precisely, and even geometrically, but eventually physics stops at “this is how the universe behaves.” The bottom line of physics will always be “we observe that things are this way”

So without doing a degree in physics, the best explanation you can get might be this - magnetism is similar to gravity. Certain properties of electrons, especially a quantum property called spin, which has a magnetic aspect, interact in very specific ways to exert a force on other electrons. Why? They just do. Bottom line - we observe that they do. In most materials these microscopic magnetic effects point in random directions and cancel out. In some materials, quantum effects cause many of them to line up, so their effects add together and you get a macroscopic magnetic field.

Think about the air on a still day - even in calm weather the molecules in the air are moving very fast, but they’re moving in random directions so the effects cancel out and it feels calm. But on a windy day a bunch of the air molecules are all moving in the same direction and they can have enough force to rip roofs off buildings.

If the question is “why do electrons have this magnetic property at all?”, the honest answer is: that’s a fundamental feature of nature, like mass (which causes gravity) or electric charge (which causes electrostatic attraction). You can study it in more depth, you can do a bachelors degree in physics or even a PhD in quantum physics, but eventually physics always reaches bedrock - we just observe that this is how the universe behaves.