Heidegger's Bible Handbook: 1 John: Recipients, Part 1
2. It was intended, not for an individual person, but for believing Jews, or rather a Church composed of Jews and Gentiles. The passage in 1 John 2:1, 2 is explained.
Since this Epistle is of the number of the Catholic Epistles, it is not inscribed to one person, or to any single Church. But it is reckoned by some to have been written to believing Jews, who appear to be addressed in 1 John 2:1, 2, in these words: My little children, these things write I unto you, that ye sin not. And if any man sin, we have an Advocate before the Father, Jesus Christ the righteous. And He is the propitiation for our sins, οὐ περὶ τῶν ἡμετέρων δὲ μόνον, ἀλλὰ καὶ περὶ ὅλου τοῦ κόσμου, and not for ours only, but also for (the sins) of the whole world. In which τεκνία, little children, and ἡμέτεροι/our appear to be used by John, who was a Jew, to distinguish believing Jews from the whole world, that is, elect believers of the Gentiles. Nevertheless, it could be said that by those words Jews are not distinguished from Gentiles, but rather that by ἡμετέρους/ours, are understood the elect consisting of Jews and Gentiles dispersed in all the earth; but by ὅλον κόσμον, the whole world, the elect yet unbelieving, scattered in all the earth, redeemed by Christ, and to be called to faith; or believers of all ages, from the beginning to the end of the world. In which sense the Epistle ought to be reckoned to be inscribed to the whole Church consisting of Jews and Gentiles, in whatever nations it might be in the the time of Saint John. For the doctrine and circumstances of the Epistle pertain indiscriminately to all believers of all nations and conditions. It is added that this writing, although it be marked as an Epistle, could be reckoned as a brief epitome of Christian doctrine, and as a succinct enchiridion of the Gospel written by John, to which certain exhortation have been added according to the common condition of the whole Church. For it does not, like the other Epistles, begin with an inscription and salutation, nor end with a salutation and prayer.