Alright I let this idea simmer with me for the whole day, hoping more
clarity would come. I think I have the gist reason for why the
electrons must be on a ecliptic plane around the nucleus of the atom.

The idea is this-- (1) atoms bond chemically in ionic, covalent,
metallic (2) that bonding requires valence electrons (3) those
electrons are the outermost electrons (4) if those valence electrons
were 3rd dimensional arranged instead of 2nd dimensional ecliptic
arranged, then they would not form a bond for they would no longer
allow ionic, covalent, metallic.

Let us look at the Lewis diagram of N2.