Note that this response has been divided into two parts: the first is the original response, and the second tries to elaborate based on a comment from the OP.

Part 1

Great question. This response includes a very brief description of some of the basic points of predestination/election, and some references with in-depth, historic information.

Here are a few main points of predestination/election, which it sounds like you may already be aware of. Again, these points are part of Reformed/"Calvinist" theology, and there are many that would disagree.

• Reformed theology emphasizes God's motivation to glorify himself, to "bring glory to his name." Note that, according to reformed theology, this does not make him selfish, because man was designed and created to worship God, so glorifying God is what is best for man. (See John Piper, & what is sometimes called "Christian Hedonism." Resources at DesigingGod.org).
• All are considered guilty in Adam, and therefore "deserve" the torment of hell (see the doctrine of "original sin").
• Because God is sovereign, he does not "owe" salvation to anyone, and would be justified in sending all of humanity to hell.
• God is glorified in the greatness of his mercy by electing some to salvation, which they cannot earn.
• God is glorified in the greatness of his wrath, by sending others to hell -- either those who are "not elect" or who are "elected to damnation" (see the doctrine of "double predestination").

Again, from the perspective of reformed theology, it is important to note that those who are predestined for salvation are in no way "deserving" of God's mercy, and there is no way to "earn" or "merit" redemption. (See the doctrines of "monergistic" vs "synergistic" regeneration).

How God has decided specifically which individuals will go to heaven is explained either as "random" or as one of the "mysteries" not revealed to man.

Some brief history and additional reference material. Your question is about the Westminster Confession and what it says about predestination; the Confession was published in 1646, but the question of predestination had been ongoing for sometime. One important document where it is addressed directly is the Canons of Dordt (sometimes "Dort"). Several followers of Arminius published a "Remonstrance" in 1610 in Holland, refuting some elements of reformed doctrine, and the Synod of Dordt was created to respond to their assertions. The Synod published their conclusions in a document called the Canons of Dordt in 1618. It is generally considered the source of the "five points of Calvinism," or "T.U.L.I.P." -- Calvin himself never actually outlined the five points in that form -- and addresses predestination in some detail, with scripture proofs. Here are two links to the Canons of Dordt, with scripture proofs: Reformed.org; CCEL. See here for a quick explanation of the history of the five points of Calvinism.

As to your question about "[w]hy or how would they justify that by using the scriptures," the Westminster Assembly included extensive scripture proofs that, in their interpretation, justified all of the statements in the Standards. A full copy of the Confession, with the original proofs, can be found on the Reformed.org page linked in your question.

Note also that you can find an in-depth, detailed discussion of the creation of the Westminster Standards in the History of the Westminster Assembly of Divines, published in 1853 by William Maxwell Hetherington.

There is also a very detailed chapter on the Westminster Standards in Philip Schaff's "Creeds of Christendom," published 1876.

Schaff's Creeds is a widely regarded, historically important book, one that is likely to be found on the bookshelves of many historians and theologians. Hetherington's work is new to me, but I see that it is linked alongside other important historical titles by sources I have found to be credible.

Part 2

In the OP's comment on 'Part 1' of this response, he gives an analogy to further clarify the question, which I'll paraphrase here: 'if, for example, 1/3 of the people on earth are predestined for heaven, why are the other 2/3 not predestined?' I've added this "Part 2" in an attempt to better address the question.

As a preface, please note that I don't claim to be an expert on predestination, but I'll try to share what I've learned.

There is what could be described as a 'subtle' difference in two basic forms of the doctrine of predestination, with the variant being described as 'double predestination,' or 'reprobation.' This doctrine says that God has predestined some to go to heaven, and others to go to hell, and that all people are predestined for one or the other. Another version is that God has predestined some to go to heaven, and has simply "passed over" the others, leaving them to be condemned by their own guilt, which they inherited from Adam and compounded through their own actions, since "all have sinned" (Rom 3:23). The end result is the same, from the perspective of the individuals and where they spend eternity; anyone who is not elected to salvation doesn't make it to heaven, according to the doctrine of predestination. Also, note that in neither case is there a "third category." In predestination, every person is either elected to salvation, or "passed over." In double predestination, every person is elected to either salvation or reprobation. Here's a work from John Bunyan that examines the doctrine of reprobation in detail.

I realize that you've stated that your question is not about predestination, but, since these matters are all intertwined, a thorough understanding of it may help to resolve your question. This C.SE post by Caleb does a great job of explaining things, and I think it's relevant to our discussion here. He also does a good job of explaining the role of substitutionary atonement, in a very concise manner -- that is, how God can offer salvation to guilty sinners who are deserving of punishment, without being unjust, although you may already understand all of that.

The question of why God has chosen a certain number of people to be saved is a matter of his sovereign will. Since he doesn't owe salvation to anyone, and no one besides Christ is capable of "earning" salvation, God can choose to have mercy on as many or as few as he chooses -- it's a free gift that he is not required to offer. An interesting reference here is Matthew 7:13-14, which tells us that "many" [ESV] will go to hell, and "few" will go to heaven, although I haven't checked the original languages on that verse. OTOMH, that's the only reference that I know of that suggests the numbers/ratios involved in who will go to heaven and who won't, although I expect there are likely references to be found in Revelation.

You might enjoy a read of Romans 9, esp. v. 19-29, and Romans 8:29.

I suppose God could have chosen to apply Christ's atonement to everyone. (Edit: See 1 Tim 2:3, a verse sometimes seen as complicating defenses of predestination). No doctrinal references that discuss the matter come to mind, and I generally seek to avoid providing my own exposition. I do know that there is nothing that would obligate him to apply Christ's atonement to all people, and that the consistent teaching is that God did not create sin, and that he remains perfectly holy and free of all guilt in choosing to bar unforgiven sinners from his paradise. Christ's atonement is sometimes described as being "sufficient" for all, but "efficient" only for the elect -- so, the infinite merit of Christ's sacrifice means that God could justly elect to salvation as many as he willed, and he chose to save a certain number, which is not disclosed to us.

This might seem to conflict with many people's understanding of God's character. It is important to remember that Reformed theology, in an effort to accurately reflect the teachings of the bible, emphasizes God's sovereignty, as well as his motivation to glorify himself.

I hope this response doesn't seem unnecessarily complicated; your question, as I understand it, seems fairly simple at first, but it actually addresses some very contentious areas of theology that have been debated for centuries. Countless sermons, treatises, and expositions have been written on the matter. I encourage you to consult some of the sources I've linked to, especially those in the second section of part 1; I'm sure they can explain things more clearly than I can, though I suppose I could still try to revise -- and hopefully shorten! -- this answer. Cheers.