> The 'white' part is just as problematic. There are many other things that make life hard too. Having a mental illness, for example, or being molested/abused as a child. Yet no one talks about non-mentally-ill privilege or unmolested privilege.

Actually yes, we do talk about that stuff as well. The things that you hear most - racial, gender, wealth and religious privilege - are talked about more simply because they affect proportionally more people.