While you state some things correctly, you fail here when you suggest that God does anything capriciously.Charlie is partially correct:
But, it ignores the larger issue.
It is certainly the case that God has no moral duty to save anyone, "elect" or "non-elect". Calvinists love to point this out. This is not the problem. It isn't so much the issue that God is seen to arbitrarily save some and not others.
It's that he even creates the ones he never intends to save in the first place.
You have to combine with Calvinism's arbitrary mechanic for who God chooses to save with the fact that no one chooses in any meaningful sense to "become" a sinner needing saving to begin with.
Calvinism assumes Original Sin, and more specifically Original Guilt whereby every human, born, unborn, died at 2, or died at 80 is a wretched being who is so filthy and disgusting in God's sight that they "deserve" eternal torture for the crime of God's decreeing that they be born with Original Sin.
This was God's plan after all.
God decided that all humans would share Adam's stain. God decided to give Adam freedom to fail knowing without a doubt he would do so. God decided that all humans would share in the guilt of that original sin Adam committed. God has decreed that all people will be born incapable of doing right or being righteous. In effect, humans are sinners because ultimately God decreed that they be sinners.
Calvinism assumes non posse non peccare:
It is simply impossible for any human God has created to NOT be a sinner.
Therefore, it is capricious at best to choose to save some and not others. God, then, has chosen, to subject countless billions to eternal torture just to glorify himself, whereas presumably, he could choose to save all. This could be argued to be evil or at least unbelievably cruel.
Couple all of this with the pretense God makes in the Scriptures about not glorying in the death of the wicked, or calling all men to repent (knowing they can't and can't want to), or claiming to have love for all mankind and it seems not only that God is being cruel but claiming to be kind and loving in the process.
Some people think this seems a lot like abusing your spouse and claiming that you are only doing so because you love them.
Or beating your wife and saying you wish: "they didn't make you have to do that".
God has a plan and purpose that is Holy ,wise,and Just in all he does. To suggest otherwise is a theological third rail.