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If God were creating a gift for His son, why would he only choose some?

Paul S has nailed it, above (even though he answered your questions with questions). There are two sides to God's character - His justice and His mercy. His purpose is to display both in creation.

Now if God is obligated to show mercy to rebels, how can we call it mercy? If He chooses to show mercy to one, how does that obligate Him to show mercy to all? And if He shows mercy to all, what of His justice?

And if God truly wants to show mercy to all, but is being thwarted by human "free will," then He is not all mighty after all.

Jesus was asked this same kind of question about the seeming unfairness of providence (see Luke 13:1-5). Where was God when the tower of Siloam fell on innocent passers-by? What about the innocent Galileans whose blood Pilate had mixed with their sacrifices? Christ's answer was a terse as the Deuteronomy passage above:

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Do you suppose that these Galileans were greater sinners than all other Galileans because they suffered this fate? I tell you, no, but unless you repent, you will all likewise perish. Or do you suppose that those eighteen on whom the tower in Siloam fell and killed them were worse debtors than the men who live in Jerusalem? I tell you, no, but unless you repent, you will all likewise perish (Luke 13:2-5, NASB).

The Galileans and victims of the Siloam tower collapse were not innocent victims who deserved better than they got, according to Jesus. They all deserved what they received. NO ONE IS INNOCENT, and God is under no obligation to show mercy to anyone.

The wonder is not that God shows mercy to some and justice to the rest. The wonder is that God shows mercy to anyone at all!

Only once in history has an innocent ever suffered.

If any act of God should truly offend us, the Cross is it. A completely innocent, totally pure, sinless and perfect Man suffered and died for the wrongdoing of others.

Was that unfair? Absolutely yes. Yet was God unjust? Absolutely not.