We have been told repeatedly that this passage, 1 John 2:2 proves universal atonement.
1Jn 2:2 He is the propitiation for our sins, and not for ours only but also for the sins of the whole world. (ESV)
You may or may not agree with my exegesis below, and accuse me of misreading, or making it too complicated. So be it. We cannot just make assertions about Scripture, we have to study and meditate and pray on it, and try to understand the full meaning of it in the context of the whole counsel of Scripture. If that means going past a superficial reading, then we must do so, since we are to handle the Word of God with care and reverence, and not as some newspaper comic strip.
There are a few things at work here, and Arminians want to continuously appeal to a "simple reading" of the text. We believe we are rendering a simple reading of the text, and we should also agree that it cannot say something different or contradictory to what is mentioned in the direct context, the context of NT soteriology, the work and offices of Christ and what John says elsewhere.
Now to be honest, and Arminains may very well have a small stroke here, they don't believe either that "world" here means "world". Because they keep adding a qualifier, and that qualifier is "faith". So really what they are saying is that Jesus was the propitiation of the sins of the world, but by world they mean "those who have heard the gospel and believe, and have faith". If that is not the case, and I am misrepresenting them, then we are left with the options that they are either saying that propitiation doesn't really mean propitiation, or they are universalists.
To understand what propitiation means, we need to see where it comes from. It means, from the Greek, "to appease anger". What anger is being appeased? The anger of God against sin, as seen from the time of the fall. To understand the role of Jesus in appeasing this anger, we need to look to where there is a very complete description of the whole history of atonement, which includes appeasing God by blood. The role of Jesus as a High Priest, after the order of Melchizedek, is found in Hebrews, and directly relates to propitiation as established through the eternal decree of God, through both the OT and NT. We find that whole description in Hebrews 7-10. I can get into more detail about that if needed, but I would ask that people go and read that for themselves, since it is too long to quote here. What is abundantly clear from that section of Scripture is that God was fully appeased by the blood that Christ shed. He is no longer angry, and Christ stands between us and God as the offering that appeased God. Jesus completely satisfied and appeased God, nothing else is needed, no more blood, no more priests. Jesus is the last one, and He still holds the office of High Priest, and will do so eternally.
In there we find that the propitiation was done once, and there is no need to do it again.
Heb 9:28 so Christ, having been offered once to bear the sins of many, will appear a second time, not to deal with sin but to save those who are eagerly waiting for him. (ESV)
Note that the plain reading here says "the sins of many", and since this is directly relevant to the propitiation, this sets some context for how we should read "world" in 1 John 2:2. This rendering could agree with that of the Arminian, which is "those who believed", the "many" for which Christ poured out His blood (Matt 26:28), which of course, takes us back to Hebrews 7-10 and the required blood offering for appeasement and atonement.
We may then read "world" here as is the case in some other places where "world" is used, as something other than "every person in the human race", as we see from the context and the subject of the verse, which is propitiation, the blood offer to appease the anger of God.
There is no reading a Calvinist presupposition into it, as some may argue. Who is John talking to here? The specific audience is not known, but we can easily see that it is a group of Christians, from the early part of 1 John 1. He is arguing here against docetism, a belief that denied that Christ came in the flesh, and held by some gnostic groups in Asia Minor. With that understanding, and given his use of propitiation which John would not have misunderstood, he is saying that Jesus, having come in the flesh, and through that has fully satisfied the anger of God, is the ONLY such propitiation in the world. Those who want to be "cleansed from unrighteousness" (1:9) have nowhere else in the world to go, they must go to God through Jesus, as He is the appeasement, and that the very nature of propitiation made it necessary that Jesus come in the flesh. That God is available to do this for any ethnic group on the planet, not just the "little children" that John is addressing here, prohibits John's own audience, not the docetists, from claiming Jesus as high priest as their exclusive property. Jesus is the High priest for all those who believe in Him.(Jo 10:14-16, 25-29).
This clearly shows that this verse cannot mean what is asserted, that is means Christ did for all the sins of all people, unless one is a universalist, or change the very meaning of propitiation, disregarding Heb 7-10 in the process.