Sin and abiding
'If we say we have no sin, we deceive ourselves' beside 'whoever abides in him does not sin' — perfectionism, abiding-versus-practice, and two-level readings.
1 John 1:5-10
5This is the message which we have heard from him and announce to you, that God is light, and in him is no darkness at all.
6If we say that we have fellowship with him and walk in the darkness, we lie, and don’t tell the truth.
7But if we walk in the light, as he is in the light, we have fellowship with one another, and the blood of Jesus Christ, his Son, cleanses us from all sin.
8If we say that we have no sin, we deceive ourselves, and the truth is not in us.
9If we confess our sins, he is faithful and righteous to forgive us the sins, and to cleanse us from all unrighteousness.
10If we say that we haven’t sinned, we make him a liar, and his word is not in us.
1 John 3:4-9
4Everyone who sins also commits lawlessness. Sin is lawlessness.
5You know that he was revealed to take away our sins, and no sin is in him.
6Whoever remains in him doesn’t sin. Whoever sins hasn’t seen him and doesn’t know him.
7Little children, let no one lead you astray. He who does righteousness is righteous, even as he is righteous.
8He who sins is of the devil, for the devil has been sinning from the beginning. To this end the Son of God was revealed: that he might destroy the works of the devil.
9Whoever is born of God doesn’t commit sin, because his seed remains in him, and he can’t sin, because he is born of God.
What each tradition says
Rabbinic / Midrashic
R. Jose said every soul before departing visits Adam and blames its own wickedness, since there is no death without sin; R. Ḥanina b. Dosa said sin, not a wild ass, causes death. Others maintained that Benjamin, Amram, Jesse, and Chileab died without sin, only as a result of Adam’s weakness in yielding to the serpent.
Joseph Jacobs (1854-1916) and Judah David Eisenstein (1854-1956), The Jewish Encyclopedia, vol. 11, s.v. 'Sin' (New York: Funk & Wagnalls, 1901-1906) — section 'Original Sin' (on death and sin)
Patristic
Augustine asks what sin 1 John iii.9 means, since understanding it as all sin would contradict 1 John i.8, where if we say we have no sin we deceive ourselves. He says the sin here may be the violation of charity, since one who hates his brother is in darkness, but he may have said this rashly.
Augustine of Hippo (354-430), Ten Homilies on the First Epistle of John, Homily V (trans. H. Browne), in Nicene and Post-Nicene Fathers, ser. 1, vol. 7 (New York: Christian Literature Publishing Co., 1888) — Homily V, on 1 John iii. 9
Catholic
The Council of Trent anathematizes anyone saying that a justified person can no longer sin or lose grace, or that one who falls and sins was never truly justified. It also anathematizes anyone saying a person can avoid all sins, even venial, throughout life, except by a special privilege from God, as the Church holds for the Blessed Virgin.
The Council of Trent, Session VI (1547), The Canons and Decrees of the Council of Trent, Session VI, canon 23, in Philip Schaff (ed.), The Creeds of Christendom, vol. 2 (New York: Harper & Brothers, 1877; CCEL text) — Session VI, decree on justification, canon 23
Orthodox
No sourced position found. Checked the Confession of Dositheus (all XVIII decrees), the Synod of Jerusalem's chapters against Lucaris, and the volume's homily catena (no Eastern statement takes up the 1 John i. 8 vs iii. 9 tension; the catena quotes 1 John i. 8 only incidentally); no public-domain English text of the Greek commentators on the Catholic Epistles (Oecumenius, Theophylact).
Reformed / Protestant
Calvin denies that this passage makes God's children wholly free from all sin; rather, no one can rightly claim this distinction except those who strive from the heart to obey God. He notes the Pelagians and Catharians wrongly used it to imagine the faithful possess angelic purity in this world, an error some Anabaptists renewed.
John Calvin (1509-1564), Commentaries on the Catholic Epistles (trans. John Owen; Edinburgh: Calvin Translation Society, 1855) — Commentary on 1 John 3:9
Evangelical
Wesley says whoever is born of God by living faith does not commit sin. In that faith, God continually breathes spiritual life into the soul, and the soul breathes out love and prayer. Because the divine seed of loving faith abides in him, so long as it does he cannot sin, being inwardly and universally changed.
John Wesley (1703-1791), Explanatory Notes upon the New Testament (1755; CCEL's 'Wesley's Notes on the Bible') — Note on 1 John 3:9
Evangelical
Barnes reads 1 John 3:9 as meaning either that true Christians do not sin habitually and characteristically, or that every true Christian is absolutely perfect and never commits any sin. If the verse applies to absolute perfection, he says, it proves all Christians are perfect, not merely some. He asks who can maintain or believe John meant that.
Albert Barnes (1798-1870), Notes on the New Testament, Explanatory and Practical (ed. Robert Frew; Grand Rapids: Baker Book House, 1949-50 reprint of the 19th-c. text, CCEL) — Note on 1 John 3:9