Why does red hair go white?

The process is very likely to be the same as any other hair colour. All you're doing is losing from the hair the ability to add some colour. The colour is accounted for by different forms of melanin: the same hormone, the same chemical in the skin that makes you go brown. You just lose the ability to add that to the hair so you see the natural colour of the hair: the keratin and that's the stuff which is white.