Romans 9:14-16 meaning

Paul answers an incorrect assertion likely to be made by the competing "authorities" that God is unjust, if He in fact decided beforehand that those of faith (including Gentiles) inherit the promise, while many Israelites who are descendants of Abraham do not. 

He asks them: What shall we say then? There is no injustice in God, is there (v 14)? He follows up this question with the exclamation May it never be! (v 14). As with other objections to Paul's teaching of faith from the competing Jewish "authorities," Paul uses the scripture to refute them. We can infer that the competing Jewish "authorities" had asserted that Paul's teaching of grace superseding the Law meant that God was unjust. Paul repeats their objection and answers adamantly that God is never unjust (May it never be!). 

Paul shows that God already did something like this when He chose Jacob over Esau. God is just doing something similar by choosing faithful Gentiles over unbelieving Israelites. Paul answers the question whether God is fair. After all, Jacob and Esau weren't yet born when God decided which one to love. Neither brother had done anything to earn or lose God's favor. This demonstrates God's right to decide as He pleases. 

So now if God decides to reward Gentiles with an inheritance, that is His prerogative. God is always just, because He is God. Paul resoundingly says, "God is not unjust. He has made it clear that He gives mercy and compassion to whomever He chooses." Why? God is God. 

Throughout his letter to the Romans thus far, Paul keeps hammering the point, "It's not about keeping rules. It's not about keeping rules." Religious rules don't justify us in the presence of God. No number of deeds is enough to justify us in God's presence, only the work of Jesus can justify us in God's presence. 

Being justified in the presence of God comes through faith (John 3:14-15). Also, living righteously on a daily basis comes by faith: obeying God and living justly is accomplished through faith (Romans 1:16-17). All approval from God is a matter of mercy, because God cannot be held to any standard, and therefore there is no basis to demand from Him. 

It is interesting to note the context of Paul's quote from Exodus 33:19 in verse 15: For He says to Moses, "I will have mercy on whom I have mercy, and I will have compassion on whom I have compassion." 

The context of Exodus 33 is that the Israelites had been rescued from slavery in Egypt (by God), Moses has gone up on the mountain to talk with God, and in Exodus 32 the Israelites impatiently demand a golden idol to worship. In response, God wants to wipe them out entirely, and start His chosen nation from Moses's line. 

Moses asks God to spare the Israelites, and despite their total disregard for God's commands, God says then He will deal compassion and mercy to whom He chooses (Exodus 33:19). Despite total betrayal, God shows grace. Our default position as humans is sinfulness. We do nothing to earn God's mercy; we deserve no favor. God shows favor anyway, as He wills to show it: So then it does not depend on the man who wills or the man who runs, but on God who has mercy (v 16). 

In the same way, God showed favor to Jacob in a way He did not show to Esau. Neither deserved God's favor, but Jacob received it by inheriting the promise God gave to Abraham to father a great nation. It is important to note that the subject is the inheritance of the blessing promised to Abraham. It is clear from the earlier chapters of Romans that the grace of God to be justified in His sight is offered completely freely, with no strings, to anyone who will receive it by faith (Romans 3:21-22, 4:3). 

The Greek word "charis" is sometimes translated "grace" and other times "favor." God gives His favor to whomever He chooses, but when it comes to being justified in His sight through the blood of Jesus, clearly God offers that to mankind freely to all who believe. God also promises to give favor/grace to those who humble themselves (1 Peter 5:5). But God will decide who has humbled themselves; no one can demand of God that they met the "I am humble standard" because there is no such thing. God is God, and all favor He grants is an act of his mercy, for He owes no one anything.