Beginning with verse 6, three antithetic tests (antithetic: being in direct and unequivocal opposition) for true Christian faith are described, and all begin with If we say. John is using this method to refer to 'boasts' made by the false teachers.
All we have from you is an assertion and nothing more. When we look at John's words later in the same epistle we can see him making the same type of argument which he made at verse 6, and it is evident his method is not one of "boasts made by false teachers."
At verse 6 John is saying that if one has true fellowship with the Lord then while in that fellowship one does not and cannot sin. When the Christian is walking according to the Spirit then at that time he is free from the law of sin (Ro.8:1-2) and he will not sin.
John says the same thing when he speaks of the Christian "abiding" in Christ Jesus:
"Whosoever abideth in him sinneth not: whosoever sinneth hath not seen him, neither known him" (1 Jn.3:6).
Anyone with the slightest amount of spiritual discernment should be able to see that John is applying the same principle at 1 John 3:6 that he did at 1 John 1:6.
It is ridiculous to think as you do, that John would use an argument which you call a "boast of false teachers" and at the same time insert himself into the argument as being himself a false teacher. This is the way that we must understand the verse according to your ideas:
If we (John and other false teachers) say that we have fellowship with him, and walk in darkness, we lie, and do not the truth" (1 Jn.1:6).
According to reality and according to the "context" the word "we" can refer to Christians and no one else. But since the reality does not fit your views we are supposed to turn reason on its head and believe your idea that when John used the word "we" he was referring to himself and other false teachers.
You have quite an imagination but your ideas are not grounded in reality.
In His grace,
Jerry