Here's a better question—why are hygiene products women use sub-categorized as "feminine hygiene products"? Shouldn't they just be called "hygiene products"? This kind of separation reinforces a patriarchal society in which women are rare objects bought and sold by men who deny them agency, in which special pricing for medication and other health services put women at an economic disadvantage for no good reason. Tampons should be available in every public restroom. If a bathroom has condom dispensers, why not tampon dispensers? This is hypocrisy and it's hurting women everywhere.
Women are in need of feminine hygiene products and they should not be punished for that by paying a luxury tax for these items. These items are considered to be a necessity, such as soap. There is no reason why women should have to pay luxury tax for something that is a necessity. Instead, luxury tax should be applied somewhere else, such as for items that are not a necessity. Examples of such items would be music players, fancy computers, ear phones, or game consoles.
I believe that feminine hygiene products are just that, hygiene products. Using a tampon is no more a luxury than using toilet paper, or a tooth brush, or taking a shower. I don't think anybody would argue for taxing these essentials to proper human hygiene on the basis of them being luxuries, and the same logic applies whether a product is used by both genders, or just one.
I do not think that there should be a "luxury tax" on feminine hygiene products, such as tampons. Being a women already has it's fair share of disadvantages; having a period every month being one of them. Why in the world would you place an additional tax on something that women "have to" use once a month? Should we start a "luxury tax" on things like after shave and male razors? Just the thought of this is truly aggravating.