1 Corinthians11chapter 11

Head covering in the first century was about honour and social signalling, and the details varied by city and class. In Roman religious practice men of rank covered their heads when sacrificing; among Jews and in much of the Greek East a respectable married woman covered hers in public. An uncovered woman in an assembly could be read as making a statement about her marriage or her availability, whatever she intended.

Paul argues from creation and from custom together, and finally appeals to the practice of the churches. Notably, he assumes throughout that women pray and prophesy in the gathering; the question is how, not whether.

The Lord's Supper was a full meal, held in a house. A well-off Roman home had a small formal dining room, the triclinium, holding perhaps nine reclining guests, and a larger open atrium for everyone else. Hosts routinely served better food and wine to the honoured few and lesser fare to the rest — a custom Roman writers themselves complained about.

Add to that the working poor and slaves arriving late, after the free were already eating, and you get exactly what Paul describes: one goes hungry while another gets drunk.