Does Romans 9:14-18 say God punishes man for what He compels man to do?
This passage does not say God causes you to sin and still hold you responsible. Here is what is actually being said, according to the light God has given me:
a) God has mercy on some people and God hardens other people for His sovereign purposes.
b) This is not injustice because those hardened get justice and giving mercy is also not injustice.
c) If God hardens a person, why does He still find fault? This question Paul addresses indirectly, the person is "finding fault" with God saying God should not punish someone whose heart God hardened. But who is the man to judge God. So even if we do not fully understand why God does what God does, we should not suppose God's actions are not just and perfect and holy.
Now, Paul could have answered the question more directly but perhaps he thought the direct answer was obvious and was being ignored on purpose, therefore he answered it as he did. But when God hardens a person's heart to bring about His purpose, the person's opportunity to obtain mercy ends, just like when a person dies, their opportunity ends. They will be punished for the wrath they piled up before God hardened their hearts, at a minimum and so God's action is obviously not injustice.
Another oft cited claim is Paul is talking about his life after he was born again in Romans chapter 7, rather than as an unregenerate. But this is pure fiction. Lets skim over the Romans chapter 7 passage. Verse 5, for while we were in the flesh... this refers to prior to being born again. If you doubt it do a search of all the times Paul uses this phrase. Verse 6, but now we have been released from the law... this refers to after being born again. Verse 7, Paul says he would not have come to know sin except through the Law... this refers to before being born again, before being released from the Law.
Now verse 9 is difficult and many misunderstand it, but what Paul is saying is he thought he was alive, not dead in his sin, when ignorant of the Law, i.e apart from the Law. But when he learned the Law, he became aware he was a covetous sinner, he knew that sin lived in him and he was therefore dead. All this revelation of his actual condition, dead in sin, occurred while he was dead in sin, i.e. prior to being born again and being made alive together with Christ.
Verse 14 again clearly indicates Paul is talking of when he was unregenerate, of the flesh, sold into bondage to sin. Thus the whole passage Romans 7:14-21 refers to Paul's wretched existence before being born again. Then in verse 24 we see how Paul was set free from this wretched condition of wishing to seek God in the inner man, but being governed by the sin in his flesh. Then in Chapter 8, verse 1, Paul says there is therefore NOW no condemnation, because he has now been born again.
Bottom line, Romans 7 refers to Paul as an unregenerate wretch man.
In summary, (1) the Bible teaches unregenerate men, in their inner man, seek to follow God, some of the time, but are unable to not sin, and therefore when they sin, they are not seeking God. There is no support in scripture for the fiction of "total spiritual inability" being the consequence of the Fall, but there is support for some men to have "total spiritual inability" (the first soil of Matthew 13), and that if a person hardens their own heart by the practice of sin, or if God hardens their heart for His purpose, their limited spiritual ability is taken away.