I suspect that originally "Hen" nights came about as the women of the tribe/village/family prepared the bride to be fit for the marriage bed (presuming her skin, brushing her hair, picking the fleas out of her dress - that sort of stuff). She wanted to be particularly lovely and delightful for her groom, because after all, their wedding night was the first time they'd Done It.
Of course, all of these excited women gossiping and warning her what she could expect and telling her that if there was any funny business she should just cancel the cheque and LTB, looked, in men's eyes, like a lot of barnyard hens flapping and squawking round a handful of corn - so it was named the "Hen Night".
Presumably the groom, celebrating with his rowdy mates, would be expected to take the opportunity to impregnate every strumpet and barmaid within reach, like a magnificent stag "tupping' his way through his herd of soft-eyed does (anybody else noticed how derogatory "hen" is, compared with the sheer magnificence of "stag?). Maybe this was so that his marital night demands weren't too terrifying for his virgin bride, seeing as he'd be shagged out from the Stag Night.*
Nowadays very few people are experiencing sexual intimacy for the first time on their wedding night. Perhaps we should just dispense with the whole ridiculous carry on altogether.
*These origins of Hen and Stag nights are pure conjecture, and probably have nothing whatsoever to do with the truth - maybe the women had a hen for their tea, and the men a stag or something. I have enjoyed speculating, though.