The Father imposed His wrath due unto, and the Son underwent punishment for, either:
1. All the sins of all men.
2. All the sins of some men, or
3. Some of the sins of all men.
In which case it may be said:
That if the last be true, all men have some sins to answer for, and so, none are saved. That if the second be true, then Christ, in their stead suffered for all the sins of all the elect in the whole world, and this is the truth. But if the first be the case, why are not all men free from the punishment due unto their sins? You answer, “Because of unbelief.” I ask, Is this unbelief a sin, or is it not? If it be, then Christ suffered the punishment due unto it, or He did not. If He did, why must that hinder them more than their other sins for which He died? If He did not, He did not die for all their sins!Owen concludes that if the first is true, then Jesus did not die for the sin of unbelief. The problem with this reasoning is that the Scriptures say that damnation is the result of unbelief. So, Owen's argument is really with the Scriptures themselves. The Scriptures never say that the damnation is the result of Jesus not dying for anyone. In fact, we have examples in Scripture of people whom the Scriptures say Jesus bought but that end up denying Christ and end up perishing. No matter how much Owen tries to make these texts say something different, it's pretty clear that anyone who held to a limited atonement would not say the things that Scripture says. There's a reason why you don't really find anyone teaching a doctrine of limited atonement until the medieval scholastic period.
The Scriptures use a variety of language to speak of Christ's atonement. Sometimes they speak of the atonement as a ransom. Some of the church fathers concluded that since in a human ransom one party must be paid for another that in the atonement Christ is paying the Devil. The Scriptures never say that Christ is paying the Devil but these church fathers pushed the picture further than Scripture does. Owen and the Calvinists essentially do the same thing with the legal language used in Scripture. In an ordinary legal setting if one person takes the place of another for punishment, the guilty person cannot be punished for the crime. But the Scriptures never teach us that if Christ suffered for someone that person will be saved on the last Day and that it would be unjust to punish that person. In Romans 5 we learn that all who died in Adam are justified in Christ and yet we learn elsewhere that this justification is received through faith which itself is a gift of God. The only way to say that someone was not justified upon the cross according to Romans 5 is to say that they did not die in Adam. The only reason given in Scripture for why someone who was justified on the cross does not receive that justification is because of unbelief.
Even Owen's argument just by itself leads to absurdity because if Christ did not die for someone it would be hard to explain how unbelief could be a sin. In the Gospel we are called to believe that Christ died for our sins. If Jesus didn't die for that person then it would be sinful for the person to believe that Jesus died for him. The doctrine of the limited atonement has the wrong starting point for doing theology. It starts from the glory of God. But Paul said he preached nothing but Christ-crucified. Christ-crucified is the central teaching of the Scriptures. If you begin with Christ-crucified you don't have to explain away what the Scriptures clearly teach and you can have confidence that Jesus really did die for you and pay for your sins. If Jesus only died for some you can never be certain you are among those for whom Jesus died because if you fall away from the faith you will just have to conclude that you never had faith to begin with.