1 John 3:9-10
No one who is born of God will continue to sin, because God's seed remains in him; he cannot go on sinning, because he has been born of God. This is how we know who the children of God are and who the children of the devil are: Anyone who does not do what is right is not a child of God; nor is anyone who does not love his brother.

     This verse is first talking about two things: Convictions, Forgiveness.
It says: No one who is born of God will continue to sin, because God's seed remains in him. Because you would know what God wants, If I have God's seed in me... or re-phrased, His words in me then I will understand and remember what God would have me do. Also, Forgivness. When we are born of God that means that we trust in Him. And when we trust in him, we are forgiven by Him. So when I recognize a sin before or after it is done, through His conviction, I will be forgiven. Or led not to sin.
Anyone who does not do what is right is not a child of God
That a tough one. But remember what the verse just said. You see if we claim God as ours and continue sinning without care, and without changing we don't have a relationship with Him. It is that simple. If I don't care that I am sinning, I can not say that I know God. That means that I would not care about God.  And finally we are to love each other! I think this is really relating our sins against God, to our sins against man. This is saying that our sins against man are still sins against God.