Although 2 Peter 3:9 literally says the Lord is "not wishing that any should perish, but that all should reach repentance" (ESV) it does not teach unlimited atonement, that is, that Jesus died for every person in the whole world.

First, the word "any" is where the focus is. Assuming this is a good translation of the word (and I have no reason to believe it is not), it does not automatically mean everyone in the whole world. In English whenever the word "any" is used, the speaker needs to stipulate which group it is referring to. In other words, one can't say "any" meaningfully unless he indicates "any of what" or "any of whom" he's referring to. If a mother says to her children that anyone can come along to the grocery store, she means only her children, not anyone in the whole world. The context makes this clear.

In this verse, Peter's context is his audience. The verse says, "The Lord is not slow to fulfill his promise as some count slowness, but is patient toward you, not wishing that any should perish, but that all should reach repentance." (Emphasis added.) So the "any" must have something to do with the "you." And we have some idea of whom "you" refers to, since at the beginning of the book Peter says he is writing to "those who have obtained a faith of equal standing with ours by the righteousness of our God and Savior Jesus Christ," that is, Christian believers. And this same chapter begins by saying this is Peter's second letter to "you, beloved," so the "you" again seems to refer to believers. Who, then are the "any"?

At first glance we might think Peter means "any" of you believers. But if people are genuine believers in Christ, then they have already reached repentance, so perhaps that is not correct.

But looking more carefully, we see that in the first chapter, verse 10, Peter has said that his audience should "be all the more diligent to confirm your calling and election." He therefore is thinking of his audience as the "elect" (and this goes along with what he says to the audience of his previous letter, "To those who are elect exiles of the Dispersion in Pontus, Galatia, Cappadocia, Asia, and Bithynia" [emphasis added]). It is therefore conceivable that he is saying that God wants all of "you, God's elect" to reach repentance--some of whom have not yet believed, but certainly will. So God is patient, gradually drawing all of his elect children to reach repentance, not wanting any of them to perish.

However, there is a second possible interpretation, which has to do with two senses of God's "will." We know that the Bible speaks of two difference senses of God's "will." We can see this in Isaiah 53:10, "Yet it was the will of the Lord to crush him...; when his soul makes an offering for guilt, ... he shall prolong his days; the will of the Lord shall prosper in his hand." The verse is about Jesus dying for our sins. The second "will" here is about obeying God's commands; Jesus obeyed God's revealed will (or "preceptive will"). The first "will" is not about that; the people who killed Jesus were sinning to do so--God was not pleased that people did that. But clearly the verse indicates that God had determined in advance that this should occur; we refer to this as part of God's secret will, his will of "decree" (that is, decreed this would occur, though God did lead the people to sin, and God is not responsible for their sin, but the sinners were responsible).

Consequently, Peter might be saying that God's revealed will is that all the people in the world would be saved, even though some do not ever repent. But this does not rule out that in God's secret will, his decretive will, some will never repent and be saved. And it does not rule out that when Jesus died, he died only for those people whom God in his decretive will chose for salvation.

Calvinists (for lack of a better term), who teach the limited-atonement view I have been describing, believe just as much as those holding to unlimited atonement that God desires everyone in the world to reach repentance, so this verse cannot be used to settle our differences, if the question is what God desires. The problem is that those holding to unlimited atonement are mistaken about God's secret will, for which I point them again to Isaiah 53:10. Additionally, I ask, if on the basis of God's desire that everyone to be saved, you insist that therefore he must have had Jesus die to pay for the sins of everyone in the world (not just the elect), then how can you not insist as well that he must also have in fact saved everyone in the world by Jesus death (what more would it require of God)? That would be universalism, which the Bible does not teach, but are you contradicting the Bible?

This verse is an explanation of why Jesus hasn't returned. He died for the elect, and his father is waiting to send Jesus to judge the world until all of the elect have been gathered, so that Jesus will receive the full reward for which he died. God is patiently waiting for his plan to unfold, and while it may seem slow to us, he is showing mercy to all the ungathered elect, and is also ensuring that Christ receives his complete reward. Not all will be saved, there are vessels created for destruction.