Why is there a loop of fabric on the back of button up shirt?

According to an internet search, that loop is also known as a "locker loop" and started out as a way to hang up shirts on a hook. It isn't relegated to just men's shirts, either. I have several shirts that also have that loop.

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Primarily for decoration today, they were originally to hang the shirt from a hook, like in a locker.

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if it is on the inside of the neck, then it is to thread a coathanger through. If on the outside of the shirt, may be just a fashion statement or a loop to hang the shirt up on a hook

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The loop allows the shirt to be hung on a hook when you don't have a coat hanger.

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There is another loop on certain dress shirts.... It is a little known fact today that when a bow tie is worn with a wing collar shirt its band should never be seen above the coat's collar. Consequently, a finely tailored formal shirt will have a belt-type vertical loop stitched immediately below the collar for the specific purpose of keeping the bow tie's band -- and the backless waistcoat's neck strap -- discreetly tucked away under the jacket.

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The loop allows the shirt to be hung from a peg, should a coat hanger not be available. Maybe at the locker room of a gym or swimming pool.