Paul taught the Roman Jews about the predestination of the descendants of Abraham to be the vehicle for the salvation of mankind. He used a visual device, the Potter and the clay, to recall to scattered Israel who had called their nation. For any Jew reading Paul's letter, there is no question the clay is the nation or vehicle chosen by God to bring salvation to the world.
Sadly this understanding is lost on much of modern Christianity. Specifically it is lost on those professors of Calvinism. Because study of the Old Testament is usually quite abbreviated for most Christians, they cannot see the direct parallels in Paul's teaching, and even his citations from the Old Testament are forgotten. For example, Romans 9:20
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?
This is a citation from Isaiah 45:9
Shall the clay say to him that fashioneth it, What makest thou? or thy work, He hath no hands?
Moreover, the passage is a very specific reference to God's use of Israel to save and bless all humankind: Is 45:15-17
15 Verily thou [art] a God that hidest thyself, O God of Israel, the Saviour. 16 They shall be ashamed, and also confounded, all of them: they shall go to confusion together [that are] makers of idols. 17 [But] Israel shall be saved in the LORD with an everlasting salvation: ye shall not be ashamed nor confounded world without end.
What's more, Paul's citation of this Passage in Isaiah parallels Isaiah referencing the downtrodden condition of the nation of Egypt:
14 Thus saith the LORD, The labour of Egypt, and merchandise of Ethiopia and of the Sabeans, men of stature, shall come over unto thee, and they shall be thine: they shall come after thee; in chains they shall come over, and they shall fall down unto thee, they shall make supplication unto thee, [saying], Surely God [is] in thee; and [there is] none else, [there is] no God. Isaiah 45:14
Since few people reading the Bible these days do the kind of scripture study to find out the context of these verses, many are confused, thinking God has chosen specific people for salvation, condemning others out of his unknowable wisdom. The context of these passages is clearly not about individual salvation.
In verse 21 he makes clear allusion to Jeremiah 18:6. Here are the two passages for comparison:
Romans 9:21 Hath not the potter power over the clay, of the same lump to make one vessel unto honour, and another unto dishonour?
Jeremiah 18:6 O house of Israel, cannot I do with you as this potter? saith the LORD. Behold, as the clay [is] in the potter's hand, so [are] ye in mine hand, O house of Israel.
The Greek New Testament by Nestle Aland cites this passage as the source of Paul's words/thoughts here. Adam Clarke in his commentary makes the same point, that Paul's discussion is about the Nation of Israel, not individuals. Reading the commentaries by the Calvinists, however, we find they very often do not offer any analysis of the underlying passages to which Paul is referring (see JFB and Matthew Henry and Calvin, for example).
While Paul refers to God hardening the heart of Pharoah, he also notes that Pharoah hardened his heart. In much the same way rain can make a field grow, corrupt seed can grow weeds of the same act. Thus God's demonstration of signs hardened Pharoah's heart, but could have converted another person. Personal Choice came into effect. While the clay is addressed as "O man" in questioning God, it is clear that Paul is talking about the nation of Israel and its long term salvation and blessing in this passage from his comments in Romans 9:23- 10:1, which 10:1 summarizes:
1 ¶ BRETHREN, my heart's desire and prayer to God for Israel is, that they might be saved.
The vessels are nations. The Gentiles and the Jews. Verse 25 talks about the passage in Hosea 2:23: "I will call them my people who were not my people." Individuals are saved, but the vehicle for that salvation is Israel, and the adoption into that Vessel by all peoples who act by faith.
We are the clay by adoption and birth.
I hope citing the scriptures and reasoning from them is helpful to understanding the Biblical doctrine of Predestination. Peace.