It seems that a commentary, from an Anglican source, may be useful here. I do not follow it's teaching but it is a good reminder that this thread is about the expiatory sacrifice of the Lord Jesus Christ.
1 John 2:2
And He is the propitiation] Or, And He Himself is a propitiation: there is no article in the Greek. Note the present tense throughout; ‘we have an Advocate, He is a propitiation’: this condition of things is perpetual, it is not something which took place once for all long ago. In His glorified Body the Son is ever acting thus. Contrast ‘He laid down His life for us’ (1Jn 3:16). Beware of the unsatisfactory explanation that ‘propitiation’ is the abstract for the concrete, ‘propitiation’ (ἱλασμός) for ‘propitiator’ (ἱλαστήρ). Had S. John written ‘propitiator’ we should have lost half the truth; viz. that our Advocate propitiates by offering Himself. He is both High Priest and Victim, both Propitiator and Propitiation. It is quite obvious that He is the former; the office of Advocate includes it. It is not at all obvious that He is the latter: very rarely does an advocate offer himself as a propitiation.
The word for ‘propitiation’ occurs nowhere in N. T. but here and in 1Jn 4:10; in both places without the article and followed by ‘for our sins’. It signifies any action which has expiation as its object, whether prayer, compensation, or sacrifice. Thus ‘the ram of the atonement’ (Num 5:8) is ‘the ram of the propitiation’ or ‘expiation’, where the same Greek word as is used here is used in the LXX. Comp. Eze 44:27; Num 29:11; Lev 25:9. The LXX. of ‘there is forgiveness with Thee’ (Psa 130:4) is remarkable: literally rendered it is ‘before Thee is the propitiation’ (ὁ ἱλασμός). So also the Vulgate, apud Te propitiatio est. And this is the idea that we have here: Jesus Christ, as being righteous, is ever present before the Lord as the propitiation. With this we should compare the use of the cognate verb in Heb 2:17 and cognate substantive Rom 3:25 and Heb 9:5. From these passages it is clear that in N. T. the word is closely connected with that special form of expiation which takes place by means of an offering or sacrifice, although this idea is not of necessity included in the radical signification of the word itself. See notes in all three places.
for our sins] Literally, concerning (περἱ) our sins: our sins are the matter respecting which the propitiation goes on. This is the common form of expression in LXX. Comp. Num 29:11; Exo 30:15-16; Exo 32:30; Lev 4:20; Lev 4:26; Lev 4:31; Lev 4:35, &c. &c. Similarly, in Joh 8:46, ‘Which of you convicteth Me of sin?’ is literally, ‘Which of you convicteth Me concerning sin?’ Comp. Joh 16:8; Joh 10:33. Notice that it is ‘our sins’, not ‘our sin’: the sins which we are daily committing, and not merely the sinfulness of our nature, are the subject of the propitiation.
and not for ours only, but also for the sins of the whole world] More literally, but also for the whole world: ‘the sins of’ is not repeated in the Greek and is not needed in English. Once more we have a parallel with the Gospel, and especially with chap. 17. ‘Neither for these only do I pray, but for them also that shall believe on Me through their word … that the world may believe that Thou didst send Me … that the world may know that Thou didst send Me, and lovedst them, even as Thou lovedst Me’ (Joh 17:20-23): ‘Behold, the Lamb of God, which taketh away the sin of the world’ (Joh 1:29): ‘We know that this is indeed the Saviour of the world’ (Joh 4:24). Comp. 1Jn 4:14. S. John’s writings are so full of the fundamental opposition between Christ or believers and the world, that there was danger lest he should seem to give his sanction to a Christian exclusiveness as fatal as the Jewish exclusiveness out of which he and other converts from Judaism had been delivered. Therefore by this (note especially ‘the whole world’) and other plain statements both in Gospel (see Joh 11:51 in particular) and Epistle he insists that believers have no exclusive right to the merits of Christ. The expiatory offering was made for the whole world without limitation. All who will may profit by it: quam late peccatum, tam late propitiatio (Bengel). The disabilities under which the whole human race had laboured were removed. It remained to be seen who would avail themselves of the restored privileges. ‘The world’ (ὁ κόσμος) is another of S. John’s characteristic expressions. In his writings it generally means those who are alienated from God, outside the pale of the Church. But we should fall into grievous error if we assigned this meaning to the word indiscriminately. Thus, in ‘the world was made by Him’ (Joh 1:10) it means ‘the universe’; in ‘This is of a truth the Prophet that cometh into the world’ (Joh 6:14) it means ‘the earth’; in ‘God so loved the world’ (Joh 3:16) it means, as here, ‘the inhabitants of the earth, the human race’. But still the prevalent meaning in both Gospel and Epistle is a bad one; ‘those who have not accepted the Christ, unbelievers.’ In the Apocalypse it occurs only thrice, once in the usual sense, ‘The kingdom of the world is become the kingdom of our Lord’ (Joh 11:15), and twice in the sense of ‘the universe’ (Joh 13:8, Joh 17:8).
