Theologically, propitiation means that God's wrath against sin, demanded by His justice, is appeased on account of the death of Christ for sinners.
1) A satisfaction of God's wrath.
2) Through the a redeeming sacrifice (in this case, Jesus Christ)
Now, if God is the propitiation for the sins of the whole world (as in everyone), then God has satisfied the wrath of God of a person whether he believes or not. Nobody can go to hell since God's wrath against all sin - including unbelief as well as any violation of the 1st and 2nd Commandments - has already been satisfied through a redeeming sacrifice (Propitiaion); hence we end up with universalism.
The other option is that 1 John 2:1-2 is not speaking of everyone in the world, but to a particular group - the elect gentiles in the world (i.e. the elect outside of the region/people John was writing to)
Furthermore, there are 4 reference to propitiation in the New Testament of which the other 3 are limited to believers. (Rom. 3:25; Heb. 2:17; 1 John 2:2;4: 10)
Romans 3:25 states that God set forth Christ[i]"a propitiation through faith in his blood."[/i] From this reference it may be observed that, if Christ is a propitiation [b]"through faith,"[/b] He cannot be a propitiation to those who never have faith, and [i]"all men have not faith"[/i] (II Thess. 3:2).
Hebrews 2:17 states that Christ was made a [i]"merciful and faithful high priest in things pertaining to God, to make reconciliation for the sins of the people."[/i] In context, [i]"the people,"[/i] are identified as the [i]"children which God hath given"[/i] Christ, (v. 13), [i]"the seed of Abraham"[/i] (v. 16). Are not [i]"the people"[/i] of verse 17 also to be identified with the [i]"many sons"[/i] in verse 10 and the [i]"every man"[/i] in verse 9 for whom [i]"by the grace of God he should taste death"[/i]?
I John 4:10 reveals the motivating cause of propitiation. [i]"Herein is love, not that we loved God, but that he loved us, and sent his Son to be the propitiation for our sins."[/i] The propitiation is restricted here to the definite pronouns, [b]"we,"[/b] [b]"us,"[/b] and [b]"our"[/b]; that is, to believers, God's elect.
Therefore, it is concluded that at least three of the four major passages on propitiation are restricted in design to God's [i]ecclesia[/i].
[i]O, precious is the flow,
That makes me White as Snow
No other fount I know;[/i]
[i][b]Nothing But the Blood of Jesus[/b][/i]