On the question, “For whom did Christ die?” the answer, “for the sins of the whole world” usually needs little defence. As early English General Baptist theologian Thomas Grantham put it in 1678:
When we are bid to behold the Lamb of God, which taketh away the Sins of the World, John I. 29. Are we to except any Person in the World, or the greatest part of the World? God forbid. Are they all become guilty per force (except Adam) and have none to justify them? Where is then the Lamb? Behold here is Fire, the Wood, and the Knife, but where is the Sacrifice, may many say, if indeed the Lamb of God died not for them? But the Holy Ghost resolves the Query to the full, I John 2. 2. He is the Propitiation for our Sins, and not for ours only, but also the for Sins of the whole World. 
Still, despite such clear statements from Scripture as John 1:29 and 1 John 2:2, 5-point Calvinists embrace the view called Limited Atonement (the “L” in TULIP, also known as Definite Atonement or Particular Redemption). To get around these passages, Calvinists will stretch the language of God's Word as far as they need to. For example, when explaining 1 John 2:2 (as quoted above) leading Calvinist John Piper teaches, “The ‘whole world’ refers to the children of God scattered throughout the whole world” (Link). Of course, there are other Calvinists who would disagree. Charles Spurgeon, for example, argued against the usual Calvinistic reinterpretation of 1 Timothy 2:3-4, teaching:
What then? Shall we try to put another meaning into the text than that which it fairly bears? I trow not. You must, most of you, be acquainted with the general method in which our older Calvinistic friends deal with this text. "All men," say they,—"that is, some men": as if the Holy Ghost could not have said "some men" if he had meant some men. "All men," say they; "that is, some of all sorts of men": as if the Lord could not have said "all sorts of men" if he had meant that. The Holy Ghost by the apostle has written "all men," and unquestionably he means all men. I know how to get rid of the force of the "alls" according to that critical method which some time ago was very current, but I do not see how it can be applied here with due regard to truth. I was reading just now the exposition of a very able doctor who explains the text so as to explain it away; he applies grammatical gunpowder to it, and explodes it by way of expounding it. I thought when I read his exposition that it would have been a very capital comment upon the text if it had read, "Who will not have all men to be saved, nor come to a knowledge of the truth." [...] My love of consistency with my own doctrinal views is not great enough to allow me knowingly to alter a single text of Scripture. [...] So runs the text, and so we must read it, "God our Savior; who will have all men to be saved, and to come unto the knowledge of the truth."
Does not the text mean that it is the wish of God that men should be saved? The word "wish" gives as much force to the original as it really requires, and the passage should run thus—"whose wish it is that all men should be saved and come to a knowledge of the truth." As it is my wish that it should be so, as it is your wish that it might be so, so it is God's wish that all men should be saved; for, assuredly, he is not less benevolent than we are. (Link)
More recently, Calvinists have published what they have called “the definitive study” on Limited Atonement titled, From Heaven He Came and Sought Her: Definite Atonement in Historical, Biblical, Theological, and Pastoral Perspective. An excellent chapter-by-chapter review of this work was written by Dr David Allen, Dean of the School of Theology and Professor of Preaching at Southwestern Baptist Theological Seminary and co-editor of the book Whosoever Will: A Biblical-Theological Critique of Five-Point Calvinism (to which he also contributed the chapter on the atonement). This review was posted on his blog between June and October, 2014. I have included the full link list below.
These reviews were very helpful to me when I first left Calvinism. I recommend paying special attention to chapter 17, “Does Penal Substitution Entail Limited Atonement?”, and 18, “Limited Atonement & the Double Payment Argument”. These are common arguments, and were some of the first brought to me by my Calvinist friends, who insisted, for example, that if I didn’t believe in limited atonement I would have to give up penal substitution too. Of course, as Dr Allen demonstrates, this is not the case.
Another to read carefully is the two part review of John Piper’s closing chapter on preaching limited atonement. Here is an excerpt:
1. Piper says what is offered is offered to the “world, to everyone who hears the gospel.”
2. What is offered is not something “designed” for all.
3. What is offered to the whole world is the “absolute fullness of all that Christ achieved for his elect.”
How, by any stretch of logic, can that which Christ designed and achieved only for the elect be offered to everyone in the world?
Piper’s conclusion, “And thus definite atonement turns out to be the only ground of a fully biblical offer of the gospel,” is totally unwarranted.
This claim is astounding to me. Piper thinks that all Calvinists and non-Calvinists who affirm unlimited atonement do not have grounds for offering the gospel in a “fully biblical” manner.
Piper turns from a consideration of the validity of the universal offer to the genuineness of that offer (661-64).
First, Piper mentions those who appeal to God’s foreknowledge as problematic for the sincerity of the gospel offer. I do not know of a single Calvinist or non-Calvinist who makes the argument that the offer of salvation to all cannot be sincere since Christ knows who will accept and who will not.
The reason the offer cannot be sincere on a definite atonement scheme is because the non-elect are being offered something that does not, in fact, exist for them.
Second, Piper states that the “bottom line objection” is not what God knows, but what God desires. Piper takes the position of most Calvinists by arguing that God is able to desire something sincerely, yet nevertheless decide that what he desires will not come to pass.
But again, Piper engages in a subtle shift away from the issue at hand. The issue is not the question of God’s two wills as many affirm in Reformed theology. The issue is our offering something to the non-elect which does not exist for them to receive.
Piper never answers this question. He rather engages in futile evasions. His argument here is off point and is simply a red herring.
I might also add that it is ultimately incoherent to argue that we do not offer people the possibility of salvation. Even on the Reformed understanding of salvation, salvation for the elect is both possible and inevitable because of election and efficacious calling. Unless one wants to argue for justification in eternity or justification at the cross (Hyper-Calvinist errors), then one has to affirm Christ’s death make’s possible salvation until the point of faith when that salvation is applied to the elect.
Reviews (external links):
Introduction: Review of “From Heaven He Came and Sought Her: Definite Atonement in Historical, Biblical, Theological, and Pastoral Perspective” – Part 1
Chapter 1: “Sacred Theology and the Reading of the Divine Word” -- Review of “From Heaven He Came and Sought Her: Definite Atonement in Historical, Biblical, Theological, and Pastoral Perspective” – Part 2
- Definite Atonement in Church History
Chapter 2: Michael Haykin, “We Trust in the Saving Blood: Definite Atonement in the Ancient Church,” -- Review of “From Heaven He Came and Sought Her: Definite Atonement in Historical, Biblical, Theological, and Pastoral Perspective” – Part 3
Chapter 3: David S. Hogg, “Sufficient for All, Efficient for Some: Definite Atonement in the Medieval Church,” -- Review of “From Heaven He Came and Sought Her: Definite Atonement in Historical, Biblical, Theological, and Pastoral Perspective” – Part 4
Chapter 4: Paul Helm, “Calvin, Indefinite Language, and Definite Atonement” -- Review of “From Heaven He Came and Sought Her: Definite Atonement in Historical, Biblical, Theological, and Pastoral Perspective” – Part 5
Chapter 5: Part 6: Note: Raymond Blacketer, “Blaming Beza: The Development of Definite Atonement in the Reformed Tradition,” in From Heaven He Came and Sought Her
Chapter 6: Review – Lee Gatiss, “The Synod of Dort and Definite Atonement,” From Heaven He Came and Sought Her – Part 7
Chapter 8: Carl Trueman on John Owen, the Covenant of Redemption, and Definite Atonement – Review 9, From Heaven He Came and Sought Her
II. Definite Atonement in the Bible
Chapter 9: Review of Williamson, “Election, Atonement, and Intercession in the Pentateuch” in From Heaven He Came and Sought Her – Part 10
Chapter 10: Isaiah 53 and Limited Atonement – Review of Motyer’s chapter in From Heaven He Came and Sought Her – Part 11
Chapter 11: Is the Atonement Limited in the Synoptics and John? Review of Harmon’s Chapter in From Heaven He Came and Sought Her – Part 12
Chapter 12: Does Paul Teach Limited Atonement? Review of Gibson’s Chapter 12 in From Heaven He Came and Sought Her
Chapter 13: Review of Jonathan Gibson’s Chapter on Pauline Soteriology and Limited Atonement in From Heaven He Came and Sought Her
Chapter 14: Review of Schreiner’s Chapter “Problematic Texts for Definite Atonement in the Pastoral and General Epistles” in From Heaven He Came and Sought Her
III. Definite Atonement in Theological Perspective
Chapter 15: Review – Donald Macleod, “Definite Atonement and the Divine Decree,” in From Heaven He Came and Sought Her
Chapter 16: Limited Atonement & The Trinity – Review of Letham’s Chapter in “From Heaven He Came & Sought Her”
Chapter 17: Does Penal Substitution Entail Limited Atonement? Review of Williams’ Chapter 17 in From Heaven He Came and Sought Her
Chapter 18: Limited Atonement & the Double Payment Argument – Review of Williams’ Chapter in From Heaven He Came and Sought Her
Chapter 19: Review of Wellum’s Chapter “The New Covenant Work of Christ” in From Heaven He Came and Sought Her
Chapter 20: Review of Henri Blocher, Chapter 20, “Systematic Theology of Definite Atonement” in From Heaven He Came and Sought Her
IV. Definite Atonement in Pastoral Practice
Chapter 21: Review of Daniel Strange’s Chapter on Those Who Never Hear the Gospel in “From Heaven He Came and Sought Her”
Chapter 22: Review of Sinclair Ferguson’s Chapter on Limited Atonement & Assurance in “From Heaven He Came & Sought Her”
Chapter 23, part 1: Review of John Piper’s Chapter in “From Heaven He Came & Sought Her,” Part 1
Chapter 23, part 2: Review of John Piper’s Chapter in “From Heaven He Came & Sought Her” – Part 2
- Video Lecture: David L. Allen, “The Extent of the Atonement and Preaching, Evangelism, and Missions”, from the Biblical Studies Symposium at Liberty University.
 As quoted in J Matthew Pinson, Thomas Grantham’s Theology of the Atonement and Justification. This quote is from David Wells' endorsement.