Aside a little proof-reading, I have minor quibbles, but you left out the ONLY useful, functional definition of hell that the people that seriously study the methodological pursuit of transcendental consciousness.
Some of them are theologians, some of them philosophers, some both, and some neither.
In essence, Hell is separation of the individual from consciousness of the Divine, just as sin is that which separates the individual- obviously a voluntary, volitional act.
So, this old aphorism is so much crap because it's lost enough meaning in its condensation from a longer form that might useful, designed to implant guilt in children and stamp out individual initiative to subordinate all to the supremacy of authority, whatever its manifestations in the status quo.