Firstly, what is “sin”?
According to Strong’s Concordance, the word “sin” is translated from the Greek word “HAMARTANO” (Strong’s #264) which means “To miss the mark so as to not share in the prize. To trespass: 1) against God; 2) against Christ; 3) against people; 4) against self; 5) against masters.”
It’s this second definition that’s most important here, indeed Biblically: to trespass. Specifically against God Almighty and thus to “miss”—fall short of, God’s mark.* When John says in his first letter that “Whosoever abides in Him sins not” (1JN 3:6.1), and “Whosoever is born of God does not commit sin” (1JN 3:9.1), he means that those born again no longer transgress against God. Because God has forgiven them of all sin, past, present, and future (CL 2:13.1) by the blood of Jesus Christ—He no longer holds their sins against them.**
When you confess belief that Jesus is Lord and that He died and rose from the dead you are given a new, spotless spirit (2CO 5:17), and God views you ONLY as that new spirit. A spirit that cannot sin, because it has “been born of God.” (1JN 3:9.2) Now sins you commit in your body and soul are separated from your new spirit “as far as east is from west.” (PS 103:12) Sure believers still transgress against Christ, other people, and themselves, but God your Father no longer considers such trespasses in your relationship with Him.
So it is true in the highest sense of the word that as a believer you no longer sin!
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*God’s mark is Jesus the sinless one (HE 4:15), who is His glory. (RO 3:23 “For all have sinned and come short of the glory of God”).
** “If any man sin, we have an advocate with the Father, Jesus Christ the righteous: and He is the propitiation for our sins” (1JN 2:1.2-2.1)