Walter Elwell provides a summary of the arguments used to support the doctrines of particular and general atonement, respectively.
In favour of particular atonement (the doctrine that Christ died for the elect):-
1. Christ is said to have died for a specific group of people, variously called “his sheep” (John 10:11, 15), “his church” (Acts 20:28), “the elect” (Rom. 8:32–35), and “his people” (Matt. 1:21).
2. God’s intentions cannot be frustrated. If God had intended all people to be saved, all would be saved. Since all are not saved, God cannot have intended to save some.
3. If Christ died for everyone, then the sins of the unsaved would be punished twice: first, by Christ, then, by themselves. But it would be unjust for any person’s sins to be punished twice.
4. The claim that Christ died for all leads logically to universalem.
5. The doctrine of particular atonement recognises that Christ died not just to make salvation possible, but to make it actual. (Rom. 5:10; 2 Cor. 5:21; Gal. 1:4; 3:13; Eph. 1:7). Otherwise, the possibility would remain that no-one would be saved.
6. Since salvation is entirely of grace, there are no conditions to be met. If salvation were intended for everyone, then everyone would receive the gifts of repentance and faith. But, obviously, not all do receive these gifts. Therefore Chris’ts death must have been intended only for those who would repent and believe – in other words, the elect.
7. Those passages that speak of Christ having died for ‘the world’ have been misinterpreted. ‘The world’ really means the elect, or the world of believers, or all nations (i.r. not just Israel).
8. When Scripture speaks of Christ having died for all it means ‘all classes’ of people, not everyone.
In favour of general atonement (the doctrine that Christ died for everyone):-
1. This has been the historic view of the church from its earliest days. We find it in almost all of the pre-Reformation writers, and in Reformers such as Luther, Luther, Melanchthon, Bullinger, Latimer, Cranmer, Coverdale, and (arguably) in Calvin. There is also an important strand amongst Calvinists such as Moise Amyraut, Richard Baxter, John Bunyan, John Newton, and John Brown
2. When the Bible says that Christ died for all (Isaiah 53:6; 1 John 2:2; 1 Timothy 2:1–6; 4:10) it means precisely that.
3. The Bible teaches that Christ takes away the sin of the world. Especially in John, ‘the world’ means precisely the sinful, godless world. No-where does ‘the world’ mean ‘the elect’ or ‘the church’.
4. This view does not lead to universalism. It does not follow that because Christ died for all then all will be saved, for not all believe. Paul taught that Christ is the Saviour of all, but in a special sense of those who believer (1 Tim 4:10)
5. The ‘law of double jeopardy does not apply. Unbelievers are lost, not because Christ did not die for them, but because they refuse God’s offer of forgiveness.
6. No-one denies that Christ died for his people, the elect. What is denied is that Christ died only for them.
7. Christ died ‘for sinners’ (Rom. 5:6–8; 1 Tim. 1:15). Now, ‘sinner’ nowhere means ‘church’, or ‘the elect’.. It means lost humankind.
8. Only this view is consistent with the well-meant offer of the gospel. How can the gospel be sincerely offered to those for whom Christ did not die?
Evangelical Dictionary of Theology, art. ‘Atonement, Extent of’