If you think of electrons with spin as bar magnets, you know bar magnets of opposite polarity as long as they're not occupying the same spatial location don't cancel out each other's magnetic field.
So what's a more apt analogy/or math reason, or explanation for all electron paired atoms have no magnetic field?
I think you are onto the subject of
Diamagnetism and or superconductivity.
Magnetic fields always rely on current
Loops, so paired electrons do produce
Currents and magnetic fields.
Except in these materials a magnetic field is set up to oppose external magnetic fields.
They do, like any moving electric charge. Instead of asking questions like these-that are part of standard curricula in physics-it would be better to learn physics, in general and electromagnetism in particular, there are so many resources now available, for instance https://www.feynmanlectures.caltech.edu/, https://www.damtp.cam.ac.uk/user/tong/em.html, https://www.damtp.cam.ac.uk/user/tong/solidstate.html
It would be a far better investment of time and effort.
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