Let me start off by saying that I have absolutely no problem with anyone choosing to "come forward" before the congregation to confess sins, should they choose to do so, as long as their reasons for doing so are godly and good-intentioned.
(I have seen - as have some of you, I'm sure - people "come forward" for less than honorable reasons in the past. There was a sister in Christ one time who had a problem with my elders. She "came forward," confessing her sins in a letter she had written and wanted me to read to the congregation, and yet a good portion of that letter said things like, "I now choose to forgive those who have wronged me, even though they themselves have shown no signs of remorse," etc. Which was not true, in that the elders had done nothing wrong to her, and even if they had, it should have been a private matter between her and them. Needless to say, I did not read her letter, but rather thanked her for her confession and asked the congregation to pray for her.)
That said, let me also say that there is a doctrine concerning confession of sins floating around the church these days which I fear the majority of brethren believe, and that doctrine is stated like so: "As public the sin is, that is how public the confession must be." Personally, I think the idea that a public sin should be publicly confessed has many merits...but to say or even imply that it is God's will is not backed up by the totality of Scripture, at least as far as my studies have shown.
The two scriptures cited in this discussion which have to do with confession are 1 John 1:9 and James 5:16. Neither of them state nor even imply that the confession talked about in these passages REQUIRES it to be before the entire congregation.
1 John 1:9, by context, is referring to confessing sins to God rather than to brethren. Verses 5-7 and verse 10 specifically speak of God and our relationship to him and him alone, so contextually verse 9 is also referring solely to God and us. "If we confess our sins, he (God) is faithful and just to forgive us our sins..." I would like to point out that nowhere in the verse does it specify or imply that the confession of our sins that we make before God is to be done before the entire congregation. Now, would it ALLOW it? Certainly, just as it would allow a private confession between one's self and God, or one confessing a sin to God and to another Christian, or two or three Christians, etc. But does it SPECIFY that there must be human witnesses who are brethren, or how many they must be? Obviously not. Therefore, we should not add to God's Word by citing 1 John 1:9 as a proof-text for it being the will of God that a sin MUST be confessed before the entire congregation.
James 5:16 says, "Confess your sins to one another, and pray for one another..." Obviously, the confession of sins being talked about here concerns a Christian who sins confessing to his brethren. However, just as before, notice that the "one another" is general, not specific. Would "one another" ALLOW for the entire congregation? Certainly, but it would also allow for another Christian, or two or three Christians, etc. Does "one another" SPECIFY that the entire congregation must be involved? Does "your sins" SPECIFY how public or private they are? No. Therefore, we must not add to God's Word by citing James 5:16 as a proof-text showing that it is God's will that a sin MUST be confessed before the entire congregation.
Matt. 18:15ff was also cited in this discussion. But let's examine that passage carefully. In verse 15, we have a brother sinning, and yet the initiative is commanded not to him, but to the brother he sinned against. The brother he sinned against is to take the initiative and go to him. If the sinner repents after being privately rebuked, then Luke 17:4 implies that a confession of sin on the sinner's part would be required, but the only indication in both Luke 17:4 and Matt. 18:15 is that the confession would be one-on-one, only to the brother he sinned against.
And then, in Matt. 18:16, we read that no repentance is forthcoming, a second effort is made, only this time with two or three witnesses. Once again, the initiative is on the part of the one being sinned against, in that he is commanded to try again, only this time after gathering two or three witnesses for confirmation. If, say, the sinner repents after being rebuked by 3-4 of his brethren, then Luke 17:4 would imply that he would make a confession, but Matt. 18:16 would imply only that it be made to those 3-4 brethren who rebuked him.
And then, in Matt. 18:17, we read that if the sinner refuses to listen to the 3-4 brethren in the second attempt described in v. 16, only then would the church be involved. However, notice again that the iniative is given not to the sinner here, but to the one being sinned against in v. 15, and then to the church. The one being sinned against is told in v. 17 to "tell it to the church." The following phrase "and if he refuses to listen even to the church" implies that the church then took the initiative and went to the sinner to rebuke him. If the sinner then repented after being rebuked by the entire congregation, then Luke 17:4 would imply that he would then make a confession, with Matt. 18:17 implying that it would be to the entire congregation.
However, notice even then that nowhere does it specify that it would have to be to the entire congregation at once during a worship assembly, just as it also doesn't specify that the entire congregation would have to at one time rebuke this man in Matt. 18:17. In order for the church to fulfill its responsibility of Matt. 18:17, they COULD all rebuke this man at once in the worship assembly (in fact, if he still doesn't repent, then 1 Cor. 5:4-5 specifies that withdrawing of fellowship must be done when the whole church is assembled together), but there are many other ways the church could rebuke this sinner. They could come to him one by one during the week, etc. In like manner, nowhere does Matt. 18:17 or Luke 17:4 specify or imply that a repentant sinner who has first been rebuked by the entire church would HAVE to, by necessity in order to be pleasing to God, confess that he is penitent in front of the entire congregation all at once. It might be the most expedient way to do it, but the ONLY way in the sight of God? The Bible doesn't specify such, so we must not add to God's Word and say so.
Now, how does this coincide with our tradition of "as public the sin is, that's how public the confession must be," meaning that the sinner MUST "come forward" during a worship assembly? Frankly, it doesn't coincide with this at all. In my observations, if there is a sin which some or perhaps all think should be publicly confessed to on Sunday morning, the church seems to be waiting for the sinner to make the first move, when in reality the Scriptures above cite that the church should take the initiative first. How many times have you seen someone publicly, in front of the entire congregation, confess a sin AFTER that entire congregation has gone to him, encouraging him to repent? I haven't. I daresay that if there are any here who have, it's been rare, especially when compared to witnessing someone feeling divinely obligated to "come forward" before the congregation and confess a sin which most of the congregation are not even aware of.
A few years ago, during a congregational assembly, an elderly sister in Christ who was senile in some regards became upset at the elders because of a doctrinal yet expedient decision they had made. She, in front of all who were present (those who were present made up about 45% of the entire congregation), told them (unjustly) that they should resign. When it was my turn to speak, I kindly but firmly rebuked her in front of everyone. As soon as the meeting was over, she immediately came up to me and apologized, and then went to each of the elders and apologized. They accepted her apology. However, a few weeks later, I found out that there was a brother (a sound, good man) who was there who demanded that she come before the entire congregation and confess her sin. He said, "This was a public sin, and the Bible says, 'As public the sin is, that's how public the confession should be.'"
What happened? Well, the sister did give me a letter to read before the entire congregation, but at the same time it dragged out, to the chagrin of her and her family and the elders, something that, as far as Scripture is concerned, was resolved the moment she penitently confessed her fault to her God and to the ones she had wronged. There was no scriptural need for her to go in front of the entire congregation, and saying that there was (a common belief in the church today) is erroneous and adding to God's Word.
Brethren, this whole idea of "coming forward" either to announce one's desire to obey the gospel or to confess sins, is nothing more than a man-made tradition started a few hundred years ago. In and of itself, there's nothing wrong with it, but we have to be careful that we do not make the same mistakes the Pharisees made and start holding our traditions on a higher plane than God's Word (Matt. 15:1-9; Matt 23). I've heard brethren state that one has not obeyed the gospel if the entire congregation doesn't get to hear their confession of faith before their baptism, just as I've heard brethren state that one is not truly forgiven of the sin of forsaking the assembly until they have come before the entire congregation to confess that wrong. Both ideas, and those like them, are adding to God's Word, as far as I can see.
If someone with godly and good intentions wants to "come forward" to confess sins, that's great. But to say that they HAVE to or else their sin is not forgiven by God is erroneous, as far as I can tell from my own studies. That's my 2 cents.