John Chrysostom

Thus much in answer to the heretics: but we must also orderly go over the whole passage. For perhaps some one might here have doubt also, questioning with himself, what sort of a crime it was for the woman to be uncovered, or the man covered? What sort of crime it is, learn now from hence. Symbols many and diverse have been given both to man and woman; to him of rule, to her of subjection: and among them this also, that she should be covered, while he hath his head bare. …

Homily on 1 Corinthians 26 ↗

Theophylact of Ohrid

He forbids the man to have a covered head not always, but only during prayer and prophecy. He also did not simply say: with a covered head, but: having upon the head (κατά κεφαλής ἔχων), in order to abolish the covering of the head not only with clothing, but also with hair. For he who has grown out his hair also has upon his head, namely, this hair. Why then does he dishonor his head? Because he has been appointed as ruler and authority, yet he makes himself a subordinate. …

Commentary on 1 Corinthians ↗

Irenaeus

Others, again (the Montanists), that they may set at nought the gift of the Spirit, which in the latter times has been, by the good pleasure of the Father, poured out upon the human race, do not admit that aspect [of the evangelical dispensation] presented by John's Gospel, in which the Lord promised that He would send the Paraclete; but set aside at once both the Gospel and the prophetic Spirit. Wretched men indeed! …

Against Heresies Book III ↗

Thomas Aquinas

Having set forth the doctrine, he adds the admonition, the reason for which is taken from the doctrine mentioned. In regard to this he does two things: first, he gives the admonition on the man's part; secondly, on the woman's (v. 5). First, therefore, he says: It has been stated that the head of the woman is the man, but any man praying or prophesying with his head covered dishonors his head. …

Commentary on 1 Corinthians ↗