Ok, I finished READING the chapter on Limited Atonement. The doctrine of Limited Atontement is essentially that Christ's death on the cross secured the salvation of those only that were previously unconditionally elected - That when Christ died, God the Father's wrath was appeased for the sins of His elect. The reprobates, those that God was not going to save, did not receive any direct benefit from the work on the cross. Christ's blood did nothing for their sins.
This is considered by many to be the most controversial point of the system, and as a result there are many 4-point Calvinists. The problem is that the Bible on many occasions says that Christ died for the whole world. 1 John 2:2 is probably the most deifficult for the Calvinist where it says that Christ is the propitiation not just for "our" sins, but also for the sins of the "whole world." Here the definition of the world has to be meant to be referring to Gentiles, and not Jews only. There are many other verses that say that Christ died for the world, or that He is the Saviour of the wordld, etc.
Vance's suggestion is that the Calvinist misunderstands the work of the Atonement vs. the application of the atonement. He uses the illustration of the Passover (and, yes, Christ is our Passover), and explains tihat killing the Lamb was sufficient sacrifice for everyone, but that it had to be applied to the door for the house to be spared.
Calvinists would argue that if a person's sins (the non-elect) were atoned for at the cross, and then the person spent eternity in hell anyway, that would be double-jeopardy - they're paying for sins already paid for. But, like the Passover, it seems like sufficient payment was made (all the Calvinists say, Amen) yet it is not applied to a person's account until regeneration.
My understanding (ignorant as it is) is that the work of the cross did not, in time, forgive the sins. But rather when a person comes to faith in Christ, that is when the sins are forgiven, and the atonement is applied. Even Calvinists would agree that a lost person that is one of God's elect, is the child of wrath until he is saved. If his sins were already forgiven at the time of the cross, then why would he be considered a child of wrath? And beyond that, if his sins were forgiven at the cross, then truly he has no sins from which he needs to repent. I'm sure there are answers for these kinds of questions, but to me, this does not fit with the clear testimony of Scripture on this particular point.
Anyway - those are my thoughts on this chapter - 2 to go!