Is the reason why Hund's rule exists, that when electrons are in different orbitals (such as 2px, 2py, or 2pz), they are most stable (lowest energy)?
If the purpose is stability/lowest energy, wouldn't it make sense for a pair of electrons to occupy the same orbital first, before filling other ones? Because, for example, one lobe from 2px is closer to a lobe from 2py (or 2pz), than to the other lobe from 2px.
So, I'd assume that a pair electrons would likely be more further apart when both exist in the same 2px orbital (in opposite lobes), rather than when one exists in a lobe in 2px and one in 2py or 2pz, thus having the least energy and being the most stable.
Or does Hund's rule exist for a different reason, and I just have a fundamental misunderstanding?