Why should a woman go gray if it doesn't look good on them?

For one thing, what you think doesn't look good on her isn't necessarily what she things.  For another, it's a pain in the neck to dye your hair and having to keep up with the roots.  There is nothing wrong with growing old gracefully and going gray can be part of that.

Same reasons a man does. 

There's no reason why a woman should let her hair to go gray, especially if her hair is pre-mature gray

How would she stop it? It's still gray under the dye.