Here's a new article on limited atonement by Kevin DeYoung.
The reason why limited atonement is important is that it teaches an ACTUAL atonement, not a HYPOTHETICAL atonement.
Free-willers deny that the atonement actually has reconciled anyone to God, but has only provided a theoretical atonement. Reformed individuals teach that the atonement actually liberated specific individuals, and this atonement will be applied to them at the proper time.
In the free-willer view, Jesus really did not die for his sheep, but he died for all mankind. In other words, there are individuals who suffer eternal punishment whom his atonement applied to. They are being punished for their sins, even though Jesus paid the cost for them.
Note: the author has limited his words to 500 in this description, so it is not a comprehensive treatment.
https://www.thegospelcoalition.org/blogs/kevin-deyoung/theological-primer-limited-atonement/
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Theological Primer - Limited Atonement
Kevin DeYoung
The doctrine of limited atonement—the L in TULIP—teaches that Christ effectively redeems from every people “only those who were chosen from eternity to salvation” (Canons of Dort, II.8). As Ursinus explains in his commentary on the Heidelberg Catechism, Christ’s death was for everyone “as it respects the sufficiency of satisfaction which he made, but not as it respects the application thereof.” In other words, the death of Christ was sufficient to atone for the sins of the whole world, but it was God’s will that it should effectively redeem those and only those who were chosen from eternity and given to Christ by the Father.
Particular redemption is often considered a more favorable term, because the point of the doctrine is not to limit the mercy of God, but to make clear that Jesus did not die in the place of every sinner on the earth, but for his particular people. The good shepherd lays his life down, not for the goats, but for the sheep (John 10:11). This is why John 6 says Jesus came to save those the Father had given to him, and why Matthew 1:21 says he died for his people, and John 15:13 says for his friends, and Acts 20:28 says for the church, and Ephesians 5:25 says for his bride, and Ephesians 1:4 says for those chosen in Christ Jesus.
The doctrine of particular redemption is worth defining and defending because it gets to the heart of the gospel. Should we say “Christ died so that sinners might come to him”? Or, “Christ died for sinners”? Did Christ’s work on the cross make it possible for sinners to come to God? Or did Christ’s work on the cross actually reconcile sinners to God? In other words, does the death of Jesus Christ make us save-able or does it make us saved?
If the atonement is not particularly and only for the sheep, then either we have universalism—Christ died in everyone’s place and therefore everyone is saved—or we have something less than full substitution. “We are often told that we limit the atonement of Christ,” Spurgeon observed, “because we say that Christ has not made a satisfaction for all men, or all men would be saved.” But, Spurgeon argued, it is the view of the atonement that says no one in particular was saved at the cross that actually limits Christ’s death. “We say Christ so died that he infallibly secured the salvation of a multitude that no man can number, who through Christ’s death not only may be saved, but are saved, must be saved, and cannot by any possibility run the hazard of being anything but saved.”
Christ does not come to us merely saying, “I’ve done my part. I laid down my life for everyone because I have saving love for everyone in the whole world. Now, if you would only believe and come to me I can save you.” Instead he says to us, I was pierced for your transgressions. I was crushed for your iniquities (Isa. 53:5). I have purchased with my blood men for God from every tribe and language and people and nation (Rev. 5:9). I myself bore your sins in my body on the tree, so that you might infallibly die to sins and assuredly live for righteousness. For my wounds did not merely make healing available. They healed you (1 Pet. 2:24).
“Amazing love!” a great Arminian once wrote. “How can it be that you, my God, should die for me?!” Praise be to our Good Shepherd who didn’t just make our salvation possible, but sustained the anger of God in body and soul, shouldered the curse, and laid down his life for the sheep.