When he says that there is no difference between the man and the woman, he is treating of Christ’s spiritual kingdom, in which individual distinctions are not regarded, or made any account of; for it has nothing to do with the body, and has nothing to do with the outward relationships of mankind, but has to do solely with the mind — on which account he declares that there is no difference, even between bond and free. In the meantime, however, he does not disturb civil order or honorary distinctions, which cannot be dispensed with in ordinary life. Here, on the other hand, he reasons respecting outward propriety and decorum — which is a part of ecclesiastical polity.
(Commentary on 1 Cor. 11:3)
The last things to be observed is, that the Lord enjoins every one of us, in all the actions of life, to have respect to our own calling. He knows the boiling restlessness of the human mind, the fickleness with which it is borne hither and thither, its eagerness to hold opposites at one time in its grasp, its ambition. Therefore, lest all things should be thrown into confusion by our folly and rashness, he has assigned distinct duties to each in the different modes of life. And that no one may presume to overstep his proper limits, he has distinguished the different modes of life by the name of callings. Every man’s mode of life, therefore, is a kind of station assigned him by the Lord, that he may not be always driven about at random. (Institutes III.x.6)
No one will ever devote himself to doing what belongs to his place [in society or the social organism], until we have learned that we were not created for ourselves, and also that we cannot be sustained, unless others extend us a helping hand. And, once we have learned this, we must still come back to what we observed before: this natural order did not come about by chance; rather God reveals His will by it, and means to test our obedience to see if we will submit to Him. Without this reverence, we will only cooperate begrudgingly, and will always be enraged when it comes to serving our neighbors. When, however, we perceive that it is God who yokes us together, teaching us that it is not without reason that he has been pleased to join us together in this way, then we should be disposed to receive the yoke He sets upon our neck, and willingly serve them whom He obligate us to serve.
(Sermon on 1 Corinthians 11:14).