1 John 1:8,9,10

I was puzzled by 1 John 1:8 and 1 John 1:10. Verse 8 says "we have no sin" and verse 10 says "we have not sinned". I was wondering why we need two different verses, and why is verse 9 in the middle. Then I come across this imaginary conversation in article after a google search:

QUOTE
To get at the true meaning of the verse in question, let us suppose a conversation between a Christian depending, as all must, on the blood of Christ for salvation, and a self-righteous sinner, who thinks he is good enough and has no sin, consequently no need of the cleansing blood.

Christian: My friend, did you know that “if we walk in the light as He is in the light, we have fellowship one with another, and the blood of Jesus Christ His Son cleanseth us from all sin?” I have proved this to be true, and if you will come to Him as I did you may prove it for yourself, and be cleansed from all sin.

Self-Righteous: But I have no sin to be cleansed away; I have no need of the blood of Jesus.

Christian: What? You say you have no sin? “If we say that we have no sin, we deceive ourselves, and the truth is not in us.” Surely you are wrong and self-deceived. You should repent, confess your sins, and be saved, for we read in I John 1 :9. “If we confess our sins, He is faithful and just to forgive us our sins, and to cleanse us from all unrighteousness.”

Self-Righteous: But I have never sinned, and do not feel that I have anything to confess or repent of. I pay my honest debts, and treat my neighbors well, and support my family, and I believe I am just as good as anyone. I am not a sinner, and have never done anything wrong.

Christian: Surely, in saving that, you are making God a liar, for in I John 1:10 it says: “If we say that we have not sinned, we make Him. liar, and His word is not in us.”

Thus we get at the meaning of the last four verses of I John 1. The text in question, then, does not have any reference whatever to one who has been cleansed from all sin, but to one who says he has no sin to be cleansed from, when he really has sin in his heart. It is also just as applicable to the unsanctified Christian who denies the further need of cleansing.
UNQUOTE

Disclaimer:
The fact that I quote the website does mean that I endorse its stand. In the first place, I have not idea about its stand on Christianity because I have not really checked it.