“Little children” are an important aspect of how the writer develops and presents their message, which, as the OP notes, sometimes suggests they are not members of the church.
Here are the little children verses of Chapter 2:
My little children, these things I write to you, so that you may not sin. And if anyone sins, we have an Advocate with the Father, Jesus Christ the righteous. (2:1)1
I write to you, little children, Because your sins are forgiven you for His name’s sake. (2:12)
…I write to you, little children, because you have known the Father. (2:13)
Little children, it is the last hour; and as you have heard that the Antichrist is coming, even now many antichrists have come, by which we know that it is the last hour. (2:18)
And now, little children, abide in Him, that when He appears, we may have confidence and not be ashamed before Him at His coming (2:28)
Fathers and young men are only used in a small portion of the letter; while the writer continues to interject messages to little children throughout the remainder of the letter, even ending on that note:
Little children, let no one deceive you. He who practices righteousness is righteous, just as He is righteous. (3:7)
You are of God, little children, and have overcome them, because He who is in you is greater than he who is in the world. (4:4)
Little children, keep yourselves from idols. Amen. (5:21)
Most translations render these 8 verses using the same phrase “little children” obscuring the fact that the writer actually used two different words, τεκνία and παιδία, that have a similar meaning. The literal meaning of τεκνία and παιδία is young child [5040-technion] [3813-paidon]. However in this letter the writer always uses both terms metaphorically.
Some commentators see “little children” as a way the writer expresses their affection while denoting their (spiritual) paternal authority [1 John Commentaries]. That approach ignores the fact the writer uses two different terms. In addition if “little children” is a form of endearment how do they differ from the brethren and the beloved which the writer also uses? Finally, this approach does not explain and in some ways conflicts with the use of little children in relationship to the fathers and the young men.
The writer uses both “little children” terms metaphorically. That is not the case with “fathers” and “young men.” These are used in a way consistent with the meaning of each word. In that light, the writer is employing the natural family unit to elucidate an aspect of their message. Here are the four terms, listed in the sequence used and grouped to recognize the family unit:
------- Family Unit ------
τεκνία Fathers Young Men παιδία
2:13 2:13 2:13
2:14 2:14 2:18
The sequence of fathers, young men, and little children/παιδία forms the family unit and is repeated. Little children/τεκνία is not a part of this example. While the writer has used the family unit as part of their message, they have also been purposeful to exclude the little children/τεκνία from that example. This technique is maintained throughout the entire letter. Fathers, young men, and little children/παιδία are only used within the one family unit example of Chapter 2 and the little children/τεκνία is always used outside the family unit. This is one reason "little children" seem to be addressed differently within Chapter 2. This should not automatically lead to the conclusion that the τεκνία were not members of the church; after all they are still being addressed in the same letter. It does help to explain the differences in how the little children, are addressed, especially within the context of the fathers, young men, and little children sequences.
The fathers, young men, and little children/παιδία of the family unit are arranged in order of decreasing physical age. This would be consistent with the natural family: fathers with multiple children would have some older than others or the little children could be grandchildren. Yet the messages addressed to the little children in the family unit contain two important points. First, these little children (παιδία) have known the Father:
…I write to you, little children (παιδία), Because you have known the Father. (2:14)
This statement is true of both the fathers and the young men.
Next, the schism event which the necessitated the writing of the letter, is placed within the address to these little children (παιδία):
Little children (παιδία), it is the last hour; and as you have heard that the Antichrist is coming, even now many antichrists have come, by which we know that it is the last hour. They went out from us, but they were not of us; for if they had been of us, they would have continued with us; but they went out that they might be made manifest, that none of them were of us. But you have an anointing from the Holy One, and you know all things. I have not written to you because you do not know the truth, but because you know it, and that no lie is of the truth. Who is a liar but he who denies that Jesus is the Christ? He is antichrist who denies the Father and the Son. Whoever denies the Son does not have the Father either; he who acknowledges the Son has the Father also. Therefore let that abide in you which you heard from the beginning. If what you heard from the beginning abides in you, you also will abide in the Son and in the Father. And this is the promise that He has promised us—eternal life. These things I have written to you concerning those who try to deceive you. But the anointing which you have received from Him abides in you, and you do not need that anyone teach you; but as the same anointing teaches you concerning all things, and is true, and is not a lie, and just as it has taught you, you will abide in Him. (2:18-27)
As with the first statement this also is true for the fathers and young men. So while the writer has used the family unit as an example, the key points of the message of the example apply to the entire family unit. That means that in terms of the message addressed to the entire family unit, the writer is treating the fathers and the young men as little children (παιδία).
The writer of the letter is not using “little children” as a type of endearing address; rather they are using the term παιδία as in the Gospel:
But Jesus called them to Him and said, “Let the little children (παιδία) come to Me, and do not forbid them; for of such is the kingdom of God. Assuredly, I say to you, whoever does not receive the kingdom of God as a little child (παιδία) will by no means enter it.” (Luke 18:16-17)
Little children (παιδία) are those who are true disciples regardless of their age. They have known the Father (2:13); they have an anointing from the Holy One and know all things (2:20); they abide in the Son and in the Father (2:24); they have the promise of eternal life (2:25).
The writer of the letter is also employing the two little children terms as they are used in John’s Gospel which records Jesus using each term once:
τεκνία: Little children, I shall be with you a little while longer. You will seek Me; and as I said to the Jews, ‘Where I am going, you cannot come,’ so now I say to you. (John 13:33)
παιδία: Then Jesus said to them, “Children, have you any food?”… (John 21:5)
During His final meal and before all of the disciples deserted Him, Jesus addressed His disciples as τεκνία. After the crucifixion and resurrection, Jesus prepares breakfast and calls His disciples παιδία. Therefore, the two little children terms can also be used to describe a disciple:
------- Family Unit ------ ---- Disciple ----
Fathers Young Men παιδία παιδία τεκνία
2:13 2:13 2:13 2:13
2:14 2:14 2:18 2:18
In addressing the schism, the writer has used two different real life examples as key structural elements. One is the family unit. Obviously the early growing church would contain older and younger members. The other is Jesus' final night before His crucifixion when the original disciples fled and a schism within the Body of Christ occurred.
This second example forms basis for the opening of the letter:
That which was from the beginning, which we have heard, which we have seen with our eyes, which we have looked upon, and our hands have handled, concerning the Word of life— the life was manifested, and we have seen, and bear witness, and declare to you that eternal life which was with the Father and was manifested to us— that which we have seen and heard we declare to you, that you also may have fellowship with us; and truly our fellowship is with the Father and with His Son Jesus Christ. (1:1-3)
The writer is not alone as a witness to the actual events of the life, death, and resurrection of Christ Jesus. At the same time, even His original disciples betrayed, denied and left Him. The actions of the original disciples serve as primary outline to the letter. Even though they had been closest to Jesus seeing and hearing all that He did, they left Him. So the overall letter is both to encourage and warn those who remained. If those who had been closest to Jesus could succumb to the pressures of the world, no one should presume their faith in Jesus Christ is immune to attack. Τεκνία, (just as Jesus addressed His disciples the night before His death), remember these key truths:
If you sin you have Jesus Christ as, an Advocate with the Father. (2:1)
Your sins have been forgiven for His name’s sake. (2:12)
Abide in Him so you will not be ashamed before Him at His coming. (2:28)
Let no one deceive you. Practice righteousness. (3:7)
The Spirit inside you is greater than the world outside. (4:4)
Keep yourself free from idols. (5:21)
Finally, I note that given this structure, and in particular the ending, and how it alludes to the original disciples (including the writer?), this message could also be shared with those who had left. The writer has delivered a message which could be used to appeal to one who had left. That is, your departure in some ways is similar to what the original disciples did and just as they returned to the truths they had heard from the beginning, so can you. And if you return your fellowship with Jesus will be restored, just as it was with the original disciples.
- All Scripture from the New King James translation.