Because as the distance becomes smaller, for unaligned magnetic fields, they stop blending into each other and become distinct fields that eventually push away each other.

As for why two magnets don't pass through each other, as they come closer eventually the alignment breaks down because both poles exist for each atom and end up repelling each other.

Of course, Paul's exclusion principle does play a role, but as long as the two objects are rigid enough you can model this mostly well enough with a magnetic dipole at each atom.