"All" means all and that's all "all" means!
Not a few educated men have used such a careless standard of exegesis. And the same goes with the word "World," or Kosmos as used in the Greek:
"World" always means everybody!
Its unfortunate that our traditions sometimes get in the way, by which we sacrifice context and the author's intent to establish a reading of a verse or passage. Fortunately, those who engage in such eisegesis don't use this standard when approaching, let's say, the resurrection or the nature of God (I'm speaking primarily of mainstream Christianity).
With that said, let's pick up our word study. The first verse in question is 1 John 2:1-2,
"My little children, I am writing these things to you so that you may not sin. And if anyone sins, we have an Advocate/Intercessor with the Father, Jesus Christ the righteous; and He Himself is the propitiation for our sins; and not for ours only, but also for those of the whole world."
This verse is often use to substantiate universal atonement, the idea that Christ's atonement was made for every single individual who has ever lived. Its also used to substantiate universalism, the idea that every single individual who has ever lived will be saved.
The emphasis is on the phrase "whole world." Sure, most people are aware of the fact that "world" or Kosmos has a wide range of meanings in John's writings (at least a dozen). But the qualifier "whole" seems to imply, if not fully establish, that John is trying to communicate the idea that Jesus' propitiatory atonement was made on behalf of every single individual that has ever lived. What else could "whole world" mean?
Next, let's skip forward a few chapters, where we will see a familiar phrase,
"We know that we are of God, and that the whole world lies in the power of the evil one." (1 John 5:19)
"Whole world" means "every single individual who has ever lived," right? Does this mean that you, a Christian who has been justified by God and sealed with the Spirit, is under the power of the devil? Not if the previous verse is true!
"We know that no one who is born of God sins; but He who is born of God keeps him, and the evil one does not touch him." (v. 18)
You can't be "under the power of the evil one," and at the same time, the "evil one does not touch him." Does "whole world" always mean "every single individual who has ever lived?" If you want to establish universal atonement from 1 John 2:1-2, then do so with words and context.