You know what else is not tax deductible? Aspirin; something nearly everyone uses many times a year and is recommended by many doctors to prevent heart attacks (although the Food and Drug Administration says otherwise). Unless a medication is prescribed (not just recommended) by a doctor, it can’t be expensed.
Now, I agree with Valenti that tampons probably shouldn’t have a special tax, like what exists in the United Kingdom, because they’re already subject to sales tax here in the U.S.
But free just because women need them? That, along with cries for free birth control or free whatever just because we’re women stops looking like equality and more like a new class of privilege.