Jamieson, Fausset and Brown on 1 Corinthians 11:16

16. A summary close to the argument by appeal to the universal custom of the churches.

if any ... seem--The Greek also means "thinks" (fit) (compare Mt 3:9). If any man chooses (still after all my arguments) to be contentious. If any be contentious and thinks himself right in being so. A reproof of the Corinthians' self-sufficiency and disputatiousness (1Co 1:20).

we--apostles: or we of the Jewish nation, from whom ye have received the Gospel, and whose usages in all that is good ye ought to follow: Jewish women veiled themselves when in public, according to Tertullian [Estius]. The former explanation is best, as the Jews are not referred to in the context: but he often refers to himself and his fellow apostles, by the expression, "we--us" (1Co 4:9, 10).

no such custom--as that of women praying uncovered. Not as Chrysostom, "that of being contentious." The Greek term implies a usage, rather than a mental habit (Joh 18:39). The usage of true "churches (plural: not, as Rome uses it, 'the Church,' as an abstract entity; but 'the churches,' as a number of independent witnesses) of God" (the churches which God Himself recognizes), is a valid argument in the case of external rites, especially, negatively, for example, Such rites were not received among them, therefore, ought not to be admitted among us: but in questions of doctrine, or the essentials of worship, the argument is not valid [Sclater] (1Co 7:17; 14:33).

neither--nor yet. Catholic usage is not an infallible test of truth, but a general test of decency.