Question
Since Paul says, "For her hair is given her for a covering'' (1 Cor. 11:15) why the insistence on a hat if the sisters allow their hair to grow long?

SOLUTION

1. The issue at Corinth was not whether long or short hair was an acceptable covering, but whether or not the head was covered with a veil or hat. This is proven by the following:
1. ----"Every man praying or prophesying, having his head covered, dishonoureth his head" (v. 4). The distinction here is obviously not between short and long-haired brethren, but rather between men with covered and uncovered heads.
2. ---- Contentious sisters were provided with an alter­ native: either cover the head or be shorn or shaven ( v. 6). But if long hair were the intended covering, then the Apostle's alternative is meaningless.
2. "Cover" ( -ed, -ing) in the A.V. disguises the fact that different words for "to cover" are used in the Greek text. The distinction between two of these, "katakalupto" and "peribolaion" proves that a veil or head covering, and not long hair is intended. These words are as follows:
1. --- "Katakalupto" ( 'kata' = 'fully'; 'kalupto' = 'to cover up'), "to cover fully" ( Yg). This word occurs through­ out verses 5- 13 and is translated "veil" in the R.S.V.; Nestle and Marshall's "Interlinear Greek-English New Testament'' and many other versions. These translations make it plain that the issue relates to a head covering, not the growth of hair, long or short.
2. -----"Peribolaion" ('peri' =  'around'; 'ballo' =  'to throw, cast'), "something cast around" ( Y g). The long hair of a woman is her glory - like a mantle cast around ( v. 15) .(8) But this is not to be displayed in the assembly of believers before the presence of God. The intended covering in the ecclesial meeting is the  "katakalupto" ---- the head covering or veil.
3. When Paul refers to the long hair given to the woman as her glory, he is drawing a parallel with what "nature" or common-sense suggests. This can be seen from the following:

4. The mistaken interpretation (9) evident in the question results from reading verse 15 as if it were the conclusion of the argument rather than an additional appeal to common-sense by a parallel: what "nature itself teaches."

8. "Peribolaion" in Hebrews 1:12 is translated "vesture", A.V.; "mantle·. R.S.V.

9. The Emphatic Diaglott has contributed to the difficulty of verse 15 by its misleading translation. The Diaglott reads: "Because her hair has been given to her instead of a veil." The Greek preposition "anti" does not necessarily mean "instead of" and can mean "for." “For”·is the usual translation adopted. The rendering of "anti" by "instead of" as a possible alternative in this verse is rejected by some commentaries.