There seem to be two situations that have given rise to the passage under consideration:
Paul has been advised of one man's shocking behavior, apparently hiring his prostitute mother for sexual favors
it is the time of the passover/unleavened bread
He uses the Jewish practice of meticulously purging the home of leaven before partaking of the Passover meal to explain the importance of being free from "the leaven of the Pharisees which is hypocrisy". IE: pretense. He says that the Passover must not be celebrated until all the rise is eliminated from the wad of dough that they will use to prepare the meal:
1Co 5:6 Your glorying ["being inflated" ie: self-congratulation] is
not good. Know ye not that a little leaven leaveneth the whole lump?
1Co 5:7 Purge out therefore the old leaven, that ye may be a new
lump, as ye are unleavened. For even Christ our passover is sacrificed
for us:
By "new lump" he means the same wad of dough but sans inflation. The Corinthians were pretty sure that they were a very shiny penny that God was proud of because they had such great spiritual insights from such gifted teachers. But Paul urges them to rather "mourn" and be about the true purpose of the Passover practice of home cleansing:
1Co 5:13 But them that are without God judgeth. Therefore put away
from among yourselves that wicked person.
So Paul is discussing the Passover with believing Jews, not the bogus "Lord's Supper" for gentiles:
1Co 5:6 Your glorying is not good. Know ye not that a little leaven
leaveneth the whole lump? 1Co 5:7 Purge out therefore the old
leaven, that ye may be a new lump, as ye are unleavened. For even
Christ our passover is sacrificed for us: 1Co 5:8 Therefore let us
keep the feast, not with old leaven, neither with the leaven of malice
and wickedness; but with the unleavened bread of sincerity and truth.
The "feast" Paul refers to is of course passover. Paul clarifies that he is not enjoining them to entirely avoid involvement with sinners because you can't do that and still carry on in this world. Rather he says that the believers are to be actively avoiding those among their own ranks that are evidently given to these behaviors:
- fornication (whatever that means)
- love of money
- idolatry
- back-biting (verbal abuse?)
- drunkenness
- extortion (law suits?)
1Co 5:9 I wrote unto you in an epistle not to company with
fornicators: 1Co 5:10 Yet not altogether with the fornicators of
this world, or with the covetous, or extortioners, or with idolaters;
for then must ye needs go out of the world. 1Co 5:11 But now I have
written unto you not to keep company, if any man that is called a
brother be a fornicator, or covetous, or an idolater, or a railer, or
a drunkard, or an extortioner; with such an one no not to eat. 1Co
5:12 For what have I to do to judge them also that are without? do
not ye judge them that are within? 1Co 5:13 But them that are
without God judgeth. Therefore put away from among yourselves that
wicked person.
Now, this is often done incorrectly resulting in a great deal of hurt. The key word, I think, is found here:
1Co 5:11 But now I have written unto you not to keep company
[συναναμίγνυμι], if any man that is called a brother be a fornicator,
or covetous, or an idolater, or a railer, or a drunkard, or an
extortioner; with such an one no not to eat.
συναναμίγνυμι (also συναναμείγνυμι) (Hippocr.; Athen. 5, 177b ‘mix up
together’) pass. w. act. sense mingle, associate with w. dat. of pers.
(Clearch. Fgm. 19 p. 14, 19 W. [in Athen. 6, 256a]; Plut., Philop. 368
[21, 8]; Hos 7:8, cp. Ezk 20:18; Philo, Mos. 1, 278; Jos., Ant. 20,
165; Just., D. 21, 2 [for συναναμίσγεσθε Ezk 20:18]) 1 Cor 5:9
(echoing the injunctions in vs. 5f); 2 Th 3:14. Abs. 1 Cor 5:11.—DELG
s.v. μείγνυμι. M-M. TW.
Arndt, W., Danker, F. W., Bauer, W., & Gingrich, F. W. (2000). A
Greek-English lexicon of the New Testament and other early Christian
literature (3rd ed., p. 965). Chicago: University of Chicago Press.
So since Paul had already been writing to them about the subject in general about being "mixed up with" these people and sharing a meal with them his concern is evidently not about passover alone. He wants distance. Paul says they are to not be involved with them, not even [μηδέ] to eat:
1Co 5:13 But them that are without God judgeth. Therefore put away
from among yourselves that wicked person.
The key is involvement. Don't be involved. I note that there is no suggestion that one must not talk to them or pretend they don't exist.
The word "not even" is μηδέ. It can simply mean here "neither" as in "Don't get mixed up with them or eat with them" or it can be used to mean "not even":
μηδέ negative disjunctive particle (Hom.+)
① and not, but not, nor continuing a preceding negation (almost always w. μή)
ⓐ in such a way that both negatives have one verb in common: in the ptc. Mt 22:29; Mk 12:24; in the pres. subj. 1 Cor 5:8; 1J 3:18; in the impv. Mt 6:25; Lk 12:22; 1J 2:15. More than one μηδέ can also follow μή (Diod S 18, 56, 5 μὴ κατιέναι is followed by μηδέ used five times with the same verb) Mt 10:9f; Lk 14:12.
ⓑ in such a way that μή and μηδέ each has a verb for itself: introduced by ὃς ἄν (ἐάν) Mt 10:14; Mk 6:11; by ἵνα J 4:15; ὅπως Lk 16:26. Both verbs in ptc. 2 Cor 4:2; in impv. Mk 13:15; J 14:27; Ro 6:12f; Hb 12:5 (Pr 3:11). The imperatives can also be wholly or partly replaced by equivalent subjunctive forms: Mt 7:6; 23:9f; Lk 17:23; 1 Pt 3:14. Both verbs in inf. (depending on παραγγέλλω) Ac 4:18; 1 Ti 1:4; 6:17; cp. Ac 21:21. More than one μηδέ after μή (Appian, Bell. Civ. 4, 11 §42 μηδεὶς μηδένα followed by μηδέ thrice; Just., D. 112, 4 μηδέποτε and μηδέ thrice) Col 2:21; 2 Cl 4:3; cp. Ro 14:21; 1 Cor 10:7–10. The first verb can also be connected w. any compound of μή: μηδείς (Jos., Ant. 8, 395; Just., A I, 5, 1 al.) Lk 3:14; 1 Ti 5:22. μήπω Ro 9:11.
ⓒ in the apodosis of a conditional sentence εἴ τις οὐ θέλει ἐργάζεσθαι, μηδὲ ἐσθιέτω one who is unwilling to work, is not to be given anything to eat 2 Th 3:10.
② not even (X., Mem. 1, 2, 36; PMagd 28, 4 [218 B.C.]; PTebt 24, 76; Just., A I, 19, 5; Mel., HE 4, 26, 6; Ath 32, 1) preceded by ὥστε μή (or μηκέτι) Mk 3:20. μηδὲ τὰ πρὸς τὴν θύραν not even about the door Mk 2:2. μηδὲ εἰς τὴν κώμην εἰσέλθῃς do not even go into the village (before returning home) Mk 8:26. τῷ τοιούτῳ μηδὲ συνεσθίειν not even to eat with such a person 1 Cor 5:11. μηδὲ ὀνομαζέσθω ἐν ὑμῖν should not even be mentioned among you Eph 5:3. μηδὲ αὐτὸν μόνον τῆς κεφαλῆς ὄγκον not only the bulk of (his swollen) head Papias (3:2c).—M-M.
Arndt, W., Danker, F. W., Bauer, W., & Gingrich, F. W. (2000). A Greek-English lexicon of the New Testament and other early Christian literature (3rd ed., p. 647). Chicago: University of Chicago Press.
So since the word has different usages, which is the right one? My thought (which disagrees with BDAG is that since eating together is not, in that culture a trivial involvement, he doesn't want to trivialize it by saying "not even to eat". In fact, Jews never ate with gentiles or Samaritans! It was forbidden by Jewish law:
https://judaism.stackexchange.com/questions/71744/eating-with-gentiles
But Paul rebuked Peter for such hypocritical behavior:
Gal 2:11 But when Peter was come to Antioch, I withstood him to the
face, because he was to be blamed. Gal 2:12 For before that
certain came from James, he did eat with the Gentiles: but when they
were come, he withdrew and separated himself, fearing them which
were of the circumcision. Gal 2:13 And the other Jews dissembled
likewise with him; insomuch that Barnabas also was carried away with
their dissimulation. Gal 2:14 But when I saw that they walked not
uprightly according to the truth of the gospel, I said unto Peter
before them all, If thou, being a Jew, livest after the manner of
Gentiles, and not as do the Jews, why compellest thou the Gentiles to
live as do the Jews?
So I think Paul is saying:
- Boo! to believing Jews who will not eat with believing gentiles:
Isa 65:5 Which say, Stand by thyself, come not near to me; for I am
holier than thou. These are a smoke in my nose, a fire that burneth
all the day.
- Boo! to believers who eat with and get mixed up with believers of the character he described.
He certainly does not have "The Lord's Supper" in mind (he expresses his aversion to that invention in chapter 11:17ff). Instead for now he wants them to quit patting themselves on the back for their great gifts and instead mourn:
1Co 5:2 And ye are puffed up, and have not rather mourned, that he
that hath done this deed might be taken away from among you.
