"God desires all men to be saved" from a Calvinist perspective?

Your assumption "that is, the selection has nothing to do with the people themselves" is not correct. In Institutes Book I, Chapter XV, Section 8, Calvin says, "Here it would be out of place to raise the question of God's secret predestination because our present subject is not what can happen or not, but what man's nature was like." In other words, God has created a plan in which each of us lives according to the facilities, such as reason and emotion, that he has given to us. We can do no other than what our nature is. So his plan of who is elect is carried out by our own actions as he as designed. So it is his will that ultimately determines our future, but it also has everything to do with who we are.

So God's desire is that all be saved, but because of who we are we cannot all be saved while also fulfilling his plan for our purpose. It would be possible for him to save us all, but that is not his plan. Nevertheless he loves all of us and desires each of us to be saved.

It is like we have several children in a race, and we want them individually all to win. However, they cannot all win without ruining the idea of the race. Thus your quote from Ezekial simply says to the slower children, "run your best because I don't want you to lose." While you genuinely feel pain at them losing, the race is important to run, and someone has to lose.

The bigger question is fundamentally why everyone isn't going to be saved. We don't know the full answer, but some some glimpse can be had from the idea that if everyone was saved then salvation would be nearly meaningless. From Institutes Book I, Chapter II, Section 1

For until men recognize that they owe everything to God, that they are nourished by his fatherly care, that he is the Author of their every good, that they should seek nothing beyond him - they will never yield him willing service. Nay, unless they establish their complete happiness in him, they will never give themselves truly and sincerely to him.

While that might carry some tone of burden placed on us, that's not what is meant. It is simply that our nature is that unless we feel like something has been accomplished, we will simply be resentful of everything that happens to us.

With verses such as 1 Timothy 2:3-4, the exegesis of the verse needs to be looked into rather than just the direct implication of it. I do not believe it's all people, but all types of people (nationalities and races). Also, in Romans 9, specifically verse 22, it states God has objects of wrath (for example, Pharaoh in Egypt).

Apostle Paul is speaking to a predominately Jewish Church in the 1st Century and his teachings were in some capacity to unite the Jew and the Gentile in the church by removing the prejudices and presuppositions of the Jews converts who thought salvation was for the Jew only and not the Gentile. It was no small revelation that the gentiles like the Jews had become heirs to the throne with God and it was Paul's calling to bring all men under the umbrella of God's love. The love of God is for all men, but his holiness demands justice just has his love bestows Grace so we must treat each character of God with proportion to the other. God loves the sinner, but God is also Holy and therefore must condemn the sinner unless grace intercedes. God has shown that not all are chosen, but all men are called to repentance based on their innate understanding of sin and God's judgement and so are without excuse.

I will post this answer as a second post that presents a real 100% Calvinist view as observed by classical Calvinists using their preferred way of expressing their view, rather than my modern preferred way as a 95% Calvinist. The truth is many versions of Calvinism today have a slight mixture of Arminianism in them. The basic difference is that within classical Calvinism mans choice to receive Christ is predominantly and 'outcome of election' and that God 'effectively calls' all for whom Christ died, and all who he does not effectively call, Christ did not strictly die for. In some sense this means God does not effectually love all. This does not mean a Calvinist does not think God is loving and loves all, it has more to do with our understanding of what 'God's will' really means.

I refer to a classical treatment on the very subject you question by John Owen entitled 'The death of death in the death of Christ':

Most apparent, then, it is that the new covenant of grace, and the promises thereof, are all of them of distinguishing mercy, restrained to the people whom God did foreknow; and so not extended universally to all. Now, the blood of Jesus Christ being the blood of this covenant, and his oblation intended only for the procurement of the good things intended and promised thereby,—for he was the surety thereof, Heb. 7:22, and of that only,—it cannot be conceived to have respect unto all, or any but only those that are intended in this covenant.

Notice Owen arguably the leading Calvinist of his time says Christ did not die for all.

This is no uncertain matter to the Calvinist. The word all simply does not mean ‘all’ without exception. Owen lists several reasons why this is so.

First Owen argues that the

‘word all being in the Scripture most commonly used in this sense (that is, for many of all sorts)’

Second Owen argues that in the case of 1 Timothy

after he hath enjoined us to pray for all, because the Lord will have all to be saved, he expressly intimates that by all men he understandeth men of all sorts, ranks, conditions, and orders, by distributing those all into several kinds, expressly mentioning some of them, as “kings and all in authority.”

Third, Owen actually clarifies that scripture says ‘we should not pray for all’ although not quoting it he is obviously referring to 1 John 5:16.

Fourth, Owen argues that no man can resist God’s will so since not all are saved not all were willed to be saved.

Fifth, Owen argues that God would have no more to be “saved” than he would have “come to the knowledge of the truth.”

These two things are of equal latitude, and conjoined in the text. But it is not the will of the Lord that all and every one, in all ages, should come to the knowledge of the truth. Of old, “he showed his word unto Jacob, his statutes and his judgments unto Israel. He hath not dealt so with any nation: and as for his judgments, they have not known them,” Ps. 147:19, 20. If he would have had them all come to the knowledge of the truth, why did he show his word to some and not to others, without which they could not attain thereunto?

So we basically get the idea. Calvinists insist that only those who are elect before the foundations of the world will be saved. The choice to receive Christ, or not, based on a provision of salvation for all, is not the determining factor, rather it is God's will and election that counts. The concept that God provisioned for all and then we simply decide, yes or no is actually more Arminian than Calvinistic. However what complicates the issue for most is that receiving Christ is not strictly a 'work' so modern Calvinism might allow some relationship to man's choice in God's election but this concept is not really supported by classical Calvinism.

Having posted two posts to the question I should add that I actually have no objection to 100% Calvinism and do not object to saying that Christ did not die for all and even to say in some sense he does not love all. (The Bible does say: "Jacob I loved, but Esau I hated" so there is a point of distinction between loving "all" or not) But we must be careful about words for I fully support that Christ did die for all and that God does love all. To be fair we must listen fully to a persons arguments and slowly understand what they mean be each term and sense in their explanation. Although I prefer to use different terms and senses as expressed in my original post where I confess I am no longer 100% Calvinists, to be honest I actually find the alternate phrases and senses by a 100% Calvinist (when properly understood) to be virtually no different then my own. Sometimes it is simply a preferred way of saying the same thing, however some peoples preferred way can be highly confusing to others! To me and many other Calvinists one can put all salvation is God's choosing and effectual calling to the elect 'only', while believing that God in some real sense truly loves all, but refer to my second post for that 'preferred way of expressing these terms'.

To be fair to Calvin, why not go straight to the horses mouth. Calvin did not believe this kind of verse (1 Tim 2:3) implied God's desire to save every man. Here is where we discover limited atonement as proposed by Calvin and is various different ways supported by the most eminent Calvinists that have ever lived, including in my mind one of the greatest theologians ever, John Owen. (I disagree with these men that I admire but have some support in Luther, so the balance is even).

In short, as the calling is a proof of the secret election, so they whom God makes partakers of his gospel are admitted by him to possess salvation; because the gospel reveals to us the righteousness of God, which is a sure entrance into life. Hence we see the childish folly of those who represent this passage to be opposed to predestination. "If God" say they, "wishes all men indiscriminately to be saved, it is false that some are predestined by his eternal purpose to salvation, and others to perdition." They might have had some ground for saying this, if Paul were speaking here about individual men; although even then we should not have wanted the means of replying to their argument; for, although the: will of God ought not to be judged from his secret decrees, when he reveals them to us by outward signs, yet it does not therefore follow that he has not determined with himself what he intends to do as to every individual man. But I say nothing on that subject, because it has nothing to do with this passage; for the Apostle simply means, that there is no people and no rank in the world that is excluded from salvation; because God wishes that the gospel should be proclaimed to all without exception. Now the preaching of the gospel gives life; and hence he justly concludes that God invites all equally to partake salvation. But the present discourse relates to classes of men, and not to individual persons; for his sole object is, to include in this number princes and foreign nations. (John Calvin's Commentary 1 Timothy)

Even Luther took this approach before Calvin regarding this specific verse:

“God desires all men to be saved” (1 Tim. 2:4), and He gave His Son for us men and created man for eternal life. Likewise: All things exist for man, and he himself exists for God that he may enjoy Him, etc.39 These points and others like them can be refuted as easily as the first one. For these verses must always be understood as pertaining to the elect only, as the apostle says in 2 Tim. 2:10 “everything for the sake of the elect.” For in an absolute sense Christ did not die for all, because He says: “This is My blood which is poured out for you” and “for many”—He does not say: for all—“for the forgiveness of sins” (Mark 14:24, Matt 26:28) (Luther's Works Volume 25.376)

As a 90-95% Calvinist (If I was a 100% anything this might constitute idolatry!) I am persuaded to agree with Luther and Calvin with respect to these particular verses but at the same time believe that God does love all men beyond the elect and that how this pertains to free will is not as cut and dry as Calvin thought. Luther also used 1 Tim 2:4 to argue about God's general care for all mankind in a separate Volume.

See this post arguing against limited atonement

What is the Biblical argument against Limited Atonement?

I also do not think it was so cut and dry in Luther's mind, see here an argument for God even loving those 'predestined to damnation'.

Does God hate unborn children?

Strictly speaking as a Calvinists I depart from Calvin on this one point. I consider it Calvin's point of weakness and failure. So do many others who deeply identify with Calvinistic theology and who are comfortable being called by that label.

After learning a bit more, I felt compelled to answer the question myself. These answers are not universally held, but they are some that I have heard, and they seem to appeal to the text more than to presuppositions.

Answer #1: In 1 Timothy 2:4, "all men" does not mean "every single person that was ever born," but rather "all sorts of men, even kings and those in authority."

I urge, then, first of all, that petitions, prayers, intercession and thanksgiving be made for all people— for kings and all those in authority, that we may live peaceful and quiet lives in all godliness and holiness. This is good, and pleases God our Savior, who wants all people to be saved and to come to a knowledge of the truth. -1 Timothy 2:1-4, NIV

Answer #2: The context of 2 Peter 3:9 is not "every single person that was ever born," but rather "you" -- that is, the elect to whom he was addressing his letter.

The Lord is not slow about His promise, as some count slowness, but is patient toward you, not wishing for any to perish but for all to come to repentance. -2 Peter 3:9, NASB

This is a compelling argument because it would not make sense to say that God is patiently forgoing His return because He is awaiting the salvation of all who would reject Him! Clearly Peter's logic is that God is patiently forgoing His return because there are more that have yet to be saved who will eventually be saved.

Answer #3: The context of Ezekiel 18:32 is not "eternal life and eternal death" but rather "being killed or spared by the coming Babylonian forces."

This answer is particularly compelling when the meta structure of the book of Ezekiel is considered. Jerusalem was on the eve of destruction, and Ezekiel's prophetic mission in the first ~half of the book is to warn the Jews and urge their repentance -- corporately, and also individually.

Closing Thoughts: I still have a personal distaste for Calvinism, as I feel that it is misleading and seems to bypass the clear heart of God in Scripture. However, as I have learned more about hermeneutics, Calvinism, and the texts listed above, I have come to believe that the three verses listed above are not strong arguments against Calvinism, so I will need to find others to use in my crusade. :)