Deodorants and antiperspirants typically contain a myriad of chemicals which can be harmful to your health. By using these products directly on the skin, you run the risk of these chemical components being absorbed into the body.
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Aluminium, propylene glycol (petroleum based), chemical fragrances, phthalates, and parabens (synthetic preservatives) have all been linked - however tenuously - to various disease manifestations.
There are a multitude of natural deodorants on the market these days, and it's just as easy and more cost effective to make your own deodorant.