Calvinists try to use Romans chapter 9 to prove their false doctrine, but they do not read the chapter carefully and thus misunderstand it. If you read the first verses, it is speaking of those who believe.
Rom 9:4 Who are Israelites; to whom pertaineth the adoption, and the glory, and the covenants, and the giving of the law, and the service of God, and the promises;
Faith is always based on a promise. When God promised Abraham he would be the father of many nations, that was the promise. And even though Abraham was very old, he believed God.
Rom 9:6 Not as though the word of God hath taken none effect. For they are not all Israel, which are of Israel:
7 Neither, because they are the seed of Abraham, are they all children: but, In Isaac shall thy seed be called.
8 That is, They which are the children of the flesh, these are not the children of God: but the children of the promise are counted for the seed.
This is explaining that the promise to Abraham to be the father of many nations would be fulfilled by those after him who believed the promises of God.
Rom 9:9 For this is the word of promise, At this time will I come, and Sara shall have a son.
Again, this chapter is speaking of those who have faith, those who believe the promises of God.
Rom 9:10 And not only this; but when Rebecca also had conceived by one, even by our father Isaac;
11 (For the children being not yet born, neither having done any good or evil, that the purpose of God according to election might stand, not of works, but of him that calleth; ) 12 It was said unto her, The elder shall serve the younger.
13 As it is written, Jacob have I loved, but Esau have I hated.
Again, this is speaking of faith. God predestined before time began that those who believe his promises would receive eternal life. This is what election means. This gift will not be of works, but faith (but of him that calleth). Jacob believed the promises that God had given his father Isaac, Esau did not. Jacob tricked Esau into selling his birthright because Jacob believed in the blessings promised to his father. Esau sold his birthright because he did not believe God's promises.
Now, it says God will show mercy on whom he will, and show wrath on whom he will.
Rom 9:14 What shall we say then? Is there unrighteousness with God? God forbid.
15 For he saith to Moses, I will have mercy on whom I will have mercy, and I will have compassion on whom I will have compassion.
16 So then it is not of him that willeth, nor of him that runneth, but of God that sheweth mercy.
God has determined that those who come to him by faith (believeing the promises) will receive mercy. Those that try to work their way (him that willeth, nor him that runneth) will receive wrath.
You see, if you neglect to read the first part of the chapter, you will not understand the rest of the chapter. The whole chapter is contrasting those who believe versus those who try to work their way. And God has chosen to show mercy on those that believe, and show wrath on those who try to approach through works.
And this is shown in Romans chapter 10
Romans 10:1 Brethren, my heart's desire and prayer to God for Israel is, that they might be saved.
2 For I bear them record that they have a zeal of God, but not according to knowledge.
3 For they being ignorant of God's righteousness, and going about to establish their own righteousness, have not submitted themselves unto the righteousness of God.
The Jews had a zeal for God. That is a compliment. But they tried to establish their own righteousness through good works. But God doesn't want their good works, he wants faith. So they failed to submit themselves to the method God chose for salvation.
And this is what Romans 9 is talking about, in fact, Romans 10 is just a continuation of the same subject being discussed in Romans 9.
Romans 9 talks of Moses. Moses had faith in God. Go to Hebrews 11 and it tells of the great faith of Moses.
Pharoah did not believe God, even after seeing numerous miraculous plagues sent by God. At one point he almost repented.
Exo 9:27 And Pharaoh sent, and called for Moses and Aaron, and said unto them, I have sinned this time: the LORD is righteous, and I and my people are wicked.
But Pharoah was feigning belief. As soon as the plague was past, he stubbornly refused to let the Hebrews go.
Exo 9:34 And when Pharaoh saw that the rain and the hail and the thunders were ceased, he sinned yet more, and hardened his heart, he and his servants.
God gave Pharoah, many, many chances to believe. How could he not with all the miracles he saw? But, Pharoah was stubborn and hardened his own heart. So Pharoah was fit for destruction. And this is what Romans 9 is saying.
Rom 9:17 For the scripture saith unto Pharaoh, Even for this same purpose have I raised thee up, that I might shew my power in thee, and that my name might be declared throughout all the earth.
18 Therefore hath he mercy on whom he will have mercy, and whom he will he hardeneth.
19 Thou wilt say then unto me, Why doth he yet find fault? For who hath resisted his will?
20 Nay but, O man, who art thou that repliest against God? Shall the thing formed say to him that formed it, Why hast thou made me thus?
21 Hath not the potter power over the clay, of the same lump to make one vessel unto honour, and another unto dishonour?
22 What if God, willing to shew his wrath, and to make his power known, endured with much longsuffering the vessels of wrath fitted to destruction:
23 And that he might make known the riches of his glory on the vessels of mercy, which he had afore prepared unto glory,
God knew Pharoah would not believe, even when he saw God's great power. So God was just in demonstrating his wrath on Pharoah.
But notice in verse 21 it says "of the same lump". That is important, and almost always overlooked. God did not create Pharoah any different than Moses. Pharoah could have believed if he so chose. But he refused. He was full of pride. The ancient Egyptian pharoahs considered themselves to be the descendants of the gods. Pharoah was not going to listen to the God of Moses and said so.
Exo 5:2 And Pharaoh said, Who is the LORD, that I should obey his voice to let Israel go? I know not the LORD, neither will I let Israel go.
Pharoah considered himself a descendant of the gods. He was not going to listen to Moses or anyone else. He was exceedingly full of pride, and exceedingly stubborn. This is why he was fit for God to show wrath upon.
But God did not make Pharoah that way, he was made of the very same lump of Moses who chose to believe.
And the end of Romans chapter 9 shows that the whole chapter is contrasting faith versus works and that God will show mercy on those who have faith, and wrath on those who try to establish their own righteousness by works.
Rom 9:30 What shall we say then? That the Gentiles, which followed not after righteousness, have attained to righteousness, even the righteousness which is of faith.
31 But Israel, which followed after the law of righteousness, hath not attained to the law of righteousness.
32 Wherefore? Because they sought it not by faith, but as it were by the works of the law. For they stumbled at that stumblingstone;
Read the entire chapter and it will become clear to you. God has chosen to show mercy on those who believe by faith, and wrath to those who try to establish their own righteousness through works.
