Really? This is ridiculous. Men and women do buy very markedly different things in general, especially in family life. For example, men disproportionally buy technological items which contribute significantly to the stable CPI.
CPI isn't just bread and butter... if it were inflation rates would be higher. Since the government can point to easier access to quality-of-life-enriching items like computers, which fall in price for equivalent goods year over year, it can manipulate the stats and make inflation look very low. This is appropriate for an "ideal" household that buys exactly that the CPI index holds.
But on the other and someone who buys disproportionally the items that are rising faster than the CPI really does feel a higher inflation rate.
It certainly seems conceivable that women tend to buy items that are rising in price faster than the CPI more than men.
It's also possible that marketing gimmicks disproportionally target women, with clothing coming to mind for example: perhaps sticker prices rise much faster than inflation, but post-"SALE" prices don't. This is a gimmick designed to encourage buying of deep sale prices, that may play better in clothing than in other industries, and that thus women fall victim to more. But since the sticker prices rise, they're noticeable.