1 John 3:4-6
4 Everyone who sins breaks the law; in fact, sin is lawlessness. 5 But you know that he appeared so that he might take away our sins. And in him is no sin. 6 No one who lives in him keeps on sinning. No one who continues to sin has either seen him or known him.
Again John is trying to be real clear on what is sin in our lives and it's effect. The false teaching was that since you are a Christian the Law doesn't really apply anymore. Yesterday we called it "anti-nominianism", which means "against the Law". The purpose of the Law is that it judges us and shows us our need for Christ. Unless we have the law, we don't know what sin is. And the Law has no power to change us so that we can keep it.
But the Gospel is that "he who had no sin came to take away our sin". Since Jesus was sinless and perfectly kept the Law, he is the only One who could take our sin upon himself. But the key teaching today is that if we live in Jesus, we don't keep on sinning. This could be confusing, because someone might say, "Just because I am a Christian doesn't mean I won't ever sin again." And that is correct.
This is again why context is so important, because the context is that false teachers are teaching that it is okay to keep on sinning, because the law doesn't really matter anymore. You can see why this could be so detrimental to the early church. And we see this teaching seeps into the church today as well. And it tarnishes our witness to a watching world.
The key thing for why John says we cannot "keep on sinning" is that we now live in him and know him. Again he is referring to the experiential knowledge we have with Jesus, as a result of "knowing Him" in a deep and personal way. By living in Him and in the power of His Holy Spirit, he gradually changes our attitude toward sin. The difference is that as we now that we in know Him when we sin, we are convicted of our sin. When we turn back to him and repent, we do not keep sinning. That would not be the freedom that Christ promises us in Him.