To help provide some context I’ve included Fr callan’s brief summary of the entire section, followed by his comments on verses 6-8.
THE CASE OF THE INCESTUOUS MAN
1 Corinthians 5:1-13
So absorbed were the Corinthians in their party strifes that the internal perfection of Christian life and the observance of ecclesiastical discipline seem to have become to them things of secondary consideration and importance. A scandalous case of incest had occurred among them, and they were so indifferent about it as to allow the offender to remain undisturbed in the Church. For this the Apostle severely rebukes them. The danger of tolerating one scandal is that it may corrupt the whole Christian community and lead the faithful away from Christ. In a previous Epistle, now lost, the Apostle had warned the Corinthians to fly the company of fornicators; but here he explains that he meant they must avoid the company of those sinners that are members of the Church. God will judge those who are outside the jurisdiction of the Church.
6. Your glorying is not good. Know you not that a little leaven corrupteth the whole lump?
The Apostle now tells the Corinthians that their glorying in their party leaders is doubly out of place and unbecoming, since they have retained among them such a scandal as the incestuous man. So strong is the force of bad example that the presence of one sinner or serious public transgression is enough to corrupt the whole community, just as a little leaven communicates its influence to a whole mass of dough.
The Apostle uses leaven in its evil signification (Gal 5:9), while our Lord employed the term to express both good and evil influences (Matt 13:33; Luke 13:21 ; Matt 16:6; Mark 8:15).
7. Purge out the old leaven, that you may be a new paste, as you are
unleavened. For Christ our pasch is sacrificed.
Continuing the similitude of the preceding verse St. Paul here counsels the Corinthians to rid themselves and their community of all sin and sinners, like the incestuous man, as the Jews before the celebration of the Paschal feast were accustomed to cleanse their houses of all leavened bread (Exod 12:18; 13:7; Matt 26:17).
As you are unleavened, i.e., as you, by reason of your vocation and condition as Christians, are pure and holy (1:2), you should cleanse your community from all sin and sinners, so that your Church may shine anew by the splendor of its virtues.
For Christ our pasch is sacrificed, better, “hath been sacrificed” (εθυθη). The Jews were obliged to clear their houses of all leaven each year for the annual celebration of the Paschal lamb; but Christians should put away the leaven of sin forever, since Christ, their Paschal Victim, “by one oblation hath perfected forever them that are sanctified” (Heb 10:14). “Christ was the Passover, (a) because He was the Lamb slain from the foundation of the world (Apoc 13:8), of which the Paschal lamb was a type (John 19:36); (b) because His blood, sprinkled on the soul, delivers us from the destroying angel; (c) because we feed on His flesh and blood (John 6:51-57), and are thereby nourished for our escape from the land of Egypt, the house of bondage. This is why we are to purge out the old leaven, because Christ, the Paschal Lamb, has been slain, and we are bidden to keep perpetual feast on Him” (Lias).
This and the following verse afford a pretty good proof that the present letter was written at Paschal time, or perhaps during the Paschal week.
8. Therefore let us feast, not with the old leaven, nor with the leaven of malice and wickedness; but with the unleavened bread of sincerity and truth.
As Christians keep a continual Paschal feast they should eschew the old leaven, i.e., their former habits of sin and th.e company of sinful men.
Malice means simply sin; wickedness is sin accompanied by hypocrisy or guile (Theod.).
The unleavened bread of sincerity and truth, i.e., the practice of virtue and the company of virtuous men.