Single Predestination logically requires a Double Predestination, in that if God chooses one to be saved (and not another), then the one not chosen, must chosen for damnation. Basically, it eliminates Preterition in favor of Reprobation

The way to explain this is by asking the following:

1) Did God eternally predetermine the ELECT (as Calvinists interpret the meaning of “the elect”) to spend eternity in Heaven? (Every Calvinist will answer “yes.”)

2) Did God eternally predetermine the [alleged] NON-ELECT to spend eternity in Heaven? (Every Calvinist will answer “no.”)

3) Did God eternally predetermine the [alleged] NON-ELECT to spend eternity in Hell? (Here’s where some Calvinists disagree. Some will say “no,” on the basis of Matthew 25:41, while every High Calvinist will say “yes,” in being logically consistent. But for those who say “no,” the follow up question is: “Where then did God eternally predetermine the [alleged] NON-ELECT to spend eternity?”

Calvinist, George Whitefield: “For, without doubt, the doctrine of election and reprobation must stand or fall together.” (Whitefield’s Letter to Wesley, emphasis mine)

According to Calvinism, Preterition is the act by which a person is left out of the will of God, or more specifically, left out of the saving will of God, and has been passed by:

Calvinist, Phil Johnson: “Mainstream Calvinists have always emphasized that the reprobate are predestined by God’s preterition and by their own fault (i.e., because of their sin). They merit hell. In other words, their damnation is not ‘unconditional.’ The elect, by contrast, are the objects of God’s active choice, and He predestines them to heaven for His own sake, not because of anything in them. They don’t merit heaven, and they don’t unleash God’s grace by some act they perform or some choice they make. They have nothing of which to boast; God’s gracious intervention is the only reason they will be in heaven--not some divinely-foreseen goodness in them. That’s what Calvinists mean when we say election is ‘unconditional.’ So the decree of election and the decree of reprobation are not exact parallels or mirror images of one another. One is active, the other passive. Election is ‘unconditional’ in precisely the sense reprobation is not. The elect don’t get what they deserve; the reprobate do. So the reprobate cannot claim their punishment is ‘unconditional,’ or purely God’s doing; yet the elect must acknowledge that the favor God shows them is not because they met any ‘conditions’ or earned any merit.” (Notes from a Reluctant Calvinist, emphasis mine)

The Calvinistic, Westminster Confession of Faith: “III. By the decree of God, for the manifestation of his glory, some men and angels are predestinated unto everlasting life; and others foreordained to everlasting death.” Additionally, it states: “VII. The rest of mankind, God was pleased, according to the unreachable counsel of his own will, whereby he extendeth or withholdeth mercy, as he pleaseth, for the glory of his sovereign power  over his creatures, to pass by; and to ordain them to dishonor and wrath for their sin, to the praise of his glorious justice.” (Westminster Confession of Faith, III. Of God’s Eternal Decree, emphasis mine) 

John Calvin: “The Lord in His unmerited election is free and exempt from the necessity of bestowing equally the same grace on all. Rather, He passes by those whom He wills, and chooses whom He wills.” (Calvin’s New Testament Commentaries: Romans and Thessalonians, p.200, emphasis mine)

John Calvin: “When predestination is discussed, it is from the start to be constantly maintained, as I today teach, that all the reprobate are justly left in death, for in Adam they are dead and condemned.” (Concerning the Eternal Predestination of God, p.121, emphasis mine)

John Calvin: “But since his purpose is to show how much more powerful in the faithful is the grace of Christ than the curse contracted in Adam, what is there here to shake the election of those whom Christ restores to life, leaving the others to perish?” (Concerning the Eternal Predestination of God, p.152, emphasis mine)

John Calvin: “Those therefore whom God passes by he reprobates, and that for no other cause but because he is pleased to exclude them from the inheritance which he predestines to his children.”  (Institutes, Book 3, Chapter 23, Section 1, emphasis mine) 

Charles Spurgeon cites the Waldensian creed: “That God saves from corruption and damnation those whom he has chosen from the foundations of the world, not for any disposition, faith, or holiness that he foresaw in them, but of his mere mercy in Christ Jesus his Sonpassing by all the rest according to the irreprehensible reason of his own free-will and justice.” (Election, emphasis mine)

Calvinist, James White: “The wonder is not that God passes by rebel sinners and shows  His justice in their condemnation; the wonder is that in eternity past He foreknew a people, chosen them in love, and decreed their eternal salvation in their perfect Savior, Jesus Christ.” (Debating Calvinism, p.152, emphasis mine)

The Canons of Dordt: “According to which decree, he graciously softens the hearts of the elect, however obstinate, and inclines them to believe, while he leaves the non-elect in his just judgment to their own wickedness and obduracy.” (The Canons of Dordt, I. Of Divine Predestination, Article 6, emphasis mine)

Calvinist, R.C. Sproul: “God made a choice--he chose some individuals to be saved unto everlasting blessedness in heaven and others he chose to pass over, to allow them to follow the consequences of their sins into eternal torment in hell.” (Chosen By God, p.22, emphasis mine)

R.C. Sproul: “In the Reformed view God from all eternity decrees some to election and positively intervenes in their lives to work regeneration and faith by a monergistic work of grace. To the non-elect God withholds this monergistic work of grace, passing them by and leaving them to themselves.” (Double Predestination, emphasis mine)

The thorny issue here is why God would pass by people that He could otherwise save, simply by giving the same irresistible grace that He allegedly gives to others.

Dave Hunt: “Follow Calvin’s reasoning. God loves and saves only the elect; He neglects to save those whom He hasn’t elected to salvation. Incredibly, through ‘shin[ing] the light of his word on the undeserving,’ he reveals His goodness and love by withholding it from them, the better to damn them for ‘rejecting the evidence of his love.’ Such warped reasoning is an integral part of Calvinism that attempts to show that God loves those whom He could have saved but instead damns.”  (What Love is This?, p.192, emphasis mine)

Agreed, and obviously that has nothing to do with undifferentiated types, kinds or levels of love, but whether it is any legitimate kind of love whatsoever at all which passes by people that God could otherwise just as easily save. That touches upon another hot button issue that Calvinists debate with each other, and that is whether or not God has a universal saving will. Some Calvinists affirm it, like Phil Johnson, whereas others like James White, reject it.

Consider the following Winston Churchhill analogy, which attempts to explain how God may love those whom He could otherwise save, but instead wills to damn:

The problem with the analogy is that Churchhill was in a predicament. Churchhill was stuck. Churchhill was helpless to save both the city and the country at large, and was forced into having to decide between saving the city, temporarily, while giving up a key Decoder device, necessary to preserve the war effort at large. Would it be reasonable to similarly say that God was equally stuck, and forced into a thorny predicament, where God was equally helpless to both save all mankind and simultaneously achieve His purposes? Giving everyone an Irresistible Grace, just like those in the elect upper-caste, would therefore, as the logic goes, come at the cost of depriving God of maximal glory, and since God couldn’t achieve both, He opted to only give some such Irresistible Grace, so that by billions being damned, God wins.

Calvinist, Vincent Cheung: “One who thinks that God’s glory is not worth the death and suffering of billions of people has too high an opinion of himself and humanity.” (The Problem of Evil, p.10, emphasis mine)

While most attribute that sentiment to Hyper Calvinism, it really is the same issue facing every other Calvinist as well. According to Calvinism, God could have easily given everyone an Irresistible Grace, but preferred not to, since there is a higher purpose in having Hell filled to capacity so that divine attributes could be expressed more fully. In Arminianism, God, too, can save everyone unilaterally, but instead gives a sincere, bona fide offer of salvation, fully paid for, to choose to accept it or reject it, in which a person’s own choice, ultimately determines their final destination.

Question:  Do Calvinists really want to say that God could not have accomplished His goals without having billions to damn, that is, by having to decree to create, and render certain, billions of people to damn, as a display of divine attributes? 

Answer:  Ultimately, according to Calvinism, God needs billions of people to damn in order to achieve maximal glory, the same people that He could otherwise give the same Irresistible Grace that He gives to an alleged, elect caste.
Question:  What is the Calvinist doctrine of Preterition? 

Answer:  It is typically an alternative to Unconditional Reprobation. In other words, instead of God affirmatively decreeing some to Hell, God has simply left them out of the will of God, being omitted for grace, since none are owed grace.