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The God I was taught was an entity […]
For day-to-day operations, believing in such an entity is 'fine', as carrying around some more complicated idea can bog one down. Most of us don't have degrees in philosophy and metaphysics. Newtonian physics and gravity is fine for most of us as well; no need to get into Einstein.
But one shouldn't confuse mental shortcuts with actual reality.
As Aquinas explains it, God could not be a being, even the supreme being, or any other kind of "entity". This is because if he/He is one kind of entity he is not another kind of entity. And there would have to be a reason for Him being one kind and not another kind. But that reason would be external to God, and thus God's nature would thus be contingent on something other than Himself.
But then wouldn't that external reason be greater than God?
Aquinas, Contra Gentiles, I.22.8-9:
> [8] Moreover, if something can exist only when several elements come together, it is composite. But no thing in which the essence is other than the being can exist unless several elements come together, namely, the essence and the being. Hence, every thing in which the essence is other than the being is composite. But, as we have shown, God is not composite. Therefore, God's being is His essence.
> [9] Every thing, furthermore, exists because it has being. A thing whose essence is not its being, consequently, is not through its essence but by participation in something, namely, being itself. But that which is through participation in something cannot be the first being, because prior to it is the being in which it participates in order to be. But God is the first being, with nothing prior to Him. His essence is, therefore, His being.
* https://isidore.co/aquinas/english/ContraGentiles1.htm#22
> The stories that the ancient Greeks tell about Hades or Zeus or Dionysus are not true of God. Would you say that they are?
The entities of the Greek pantheon are creatures. Perhaps powerful ones, but creatures not the less. That fact we use the term "god(s)" for them as well as the Christian God is an artefact of language.
See Edward Feser's book Aquinas for a good treatment of this subject in more modern language. Trying to follow translated Latin can be slow going, and isn't really necessary unless you really want to go to primary sources—but one has to be mindful of terminology and ascribing modern interpretations to certain words used.