Being relatively new to Calvinism, still learning it and not yet fit for teaching it, I can only tell you why this teaching aided me in coming to accept the point of "Limited Atonement."
It was undeniable (to me) that the atonement could have been efficient for ALL MANKIND. I know it's theoretical. But Christ, being God, was a sufficient sacrifice for all mankind. I think the Bible bears that out. And to refute universalism, we must also recognize that the Bible is clear that the atonement is only efficacious for the elect... with that being said, I don't have a problem with the statement.
Yes, I'd also agree with that.
There's nothing more that
need be added since the Crucifixion, to save another person.
I think mqurlgw's point is that it doesn't seem to address the point under discussion, but it only comments on a more general point, dissipating the point in Reformed theology. This, if I take him to mean what Calvin meant. Calvin himself was annoyed by this bit of philosophizing:
Now we will not permit the common solution of this question to avail on the present occasion, which would have it that Christ suffered sufficiently for all men, but effectually for His elect alone. This great absurdity, by which our monk has procured for himself so much applause amongst his own fraternity, has no weight whatever with me. John does indeed extend the benefits of the atonement of Christ, which was completed by His death, to all the elect of God throughout what climes of the world soever they may be scattered. But though the case be so, it by no means alters the fact that the reprobate are mingled with the elect in the world. It is also a fact, without controversy, that Christ came to atone for the sins " of the whole world." But the solution of all difficulty is immediately at hand, in the truth and fact, that it is " whosoever believeth in Him" that " shall not perish, but shall have eternal life." For our present question is, not what the power or virtue of Christ is, nor what efficacy it has in itself, but who those are to whom He gives Himself to be enjoyed. Now if the possession of Christ stands in faith, and if faith flows from the Spirit of adoption, it follows that he alone is numbered of God among His children who is designed of God to be a partaker of Christ. Eternal Predestination, p. 165
We really need to shift to the Calvinist meaning behind the "L" to discuss this, too: namely, Definite or Particular Atonement. Even arminianism is a Limited Atonement: only universalism is an unlimited atonement.
Amyrauldianism is one way to deal with five-point Calvinism; technically it straddles the span between 4 & 5 points in hypothetical universalism.
In other words, there are real, live 4-pointers out there too, who don't accept that there're definite individuals atoned-for. I've never figured out what other points mean when this is held, though: how do you have unconditional election and an indefinite atonement?
God picks unconditionally -- and so He picks specific people. If God didn't pick specific people,
and there's not a single thing people can do to make God choose them, how would it be that not everyone's saved or condemned?
Other points are equally problematic. If the Spirit is effective at calling people, and the atonement isn't specific, why won't the Spirit be effective in calling all people to Christ?