What specific charge is brought against God in Romans 9:14?

Question

In Romans 9:14, Paul asks the question, "What then shall we say? Is God unjust?" He replies, of course, "Not at all!" And then seemingly he goes on to give a reason for why God is not unjust. However, before I can understand the argument Paul makes for why God is not unjust, it seems good to first understand why this question even arises.

What is it that is casting aspersions on the justice of God for which Paul gives an answer?

Answer 1

Paul structured Romans a bit like a Socratic dialogue with himself taking the role of the main character and a hypothetical reader being assigned the role of foil or student. Paul anticipates and articulates the reader's objections to his arguments so that he can address them. It would likely have been a well-known genre to a Roman audience since Cicero reintroduced the form.

The text that caused the "reader" to object was:

And not only so, but also when Rebekah had conceived children by one man, our forefather Isaac, though they were not yet born and had done nothing either good or bad—in order that God's purpose of election might continue, not because of works but because of him who calls—she was told, “The older will serve the younger.” As it is written, “Jacob I loved, but Esau I hated.”—Romans 9:10-13 (ESV)

(It's difficult to isolate quotes in Romans since Paul's argument flows from one idea to another so fluidly.)

A reader could object to the idea of God choosing one brother (and by implication, one people group) over another when there was no particular reason to prefer one over the other. Both "had done nothing either good or bad", so how can God justly love one and hate the other? The broader question, as seen in the new topic Paul starts at the beginning of the chapter, is how can God chose the Jewish people to receive His inheritance to the exclusion of other groups?

Paul's answer is that God can chose who He will show mercy to:

For he says to Moses, “I will have mercy on whom I have mercy, and I will have compassion on whom I have compassion.” So then it depends not on human will or exertion, but on God, who has mercy. For the Scripture says to Pharaoh, “For this very purpose I have raised you up, that I might show my power in you, and that my name might be proclaimed in all the earth.” So then he has mercy on whomever he wills, and he hardens whomever he wills.—Romans 9:15-18 (ESV)

This raises another question about whether we can fault anyone since nobody can resist His will. A series of questions in chapter 9 lead up to the point Paul wants to make in chapter 10: that it is imperative that the message of the gospel be carried to all people. All of this serves the purpose Paul sets out for himself at the start of the letter:

For I am not ashamed of the gospel, for it is the power of God for salvation to everyone who believes, to the Jew first and also to the Greek. For in it the righteousness of God is revealed from faith for faith, as it is written, “The righteous shall live by faith.”—Romans 1:16-17 (ESV)

Summary

The accusation against God in this verse is that He is unjust to chose the children of Israel to receive His inheritance.

Answer 2

¹⁰ And not only so, but also when Rebekah had conceived children by one man, our forefather Isaac, ¹¹ though they were not yet born and had done nothing either good or bad—in order that God's purpose of election might continue, not because of works but because of him who calls— ¹² she was told, “The older will serve the younger.” ¹³ As it is written, “Jacob I loved, but Esau I hated.”
¹⁴ What shall we say then? Is there injustice on God's part? By no means!   _ESV

The unspoken assumption of the imaginary 'questioner' is that it would be unjust for God to judge except on the basis of the works done by a man.

The question is a natural one for someone superficially familiar with God's dealings with his people - the law promised blessing for obedience and curse for disobedience - this can lead to the obvious conclusion that because God decided to judge on that basis in a particular context, He did so because that was the only just way - ie it would be unjust for God to judge on any other basis.

Paul goes on to destroy the very foundation of the question by denying that it would be unjust for God to judge on any other basis - but that is not the question you are asking :-)