Are you comfortable with women travelling alone?

I was browsing the interwebs today and read an article about women traveling alone.

I remembered a young woman telling me about all of these trips she had taken solo to South America. I remember I found myself admiring her, yet squicked out about the fact of “Women traveling alone and rape”. Then I felt ashamed of myself and humanity both because this was an issue.

Would you encourage a female friend to travel alone? Is this a sexist holdover I should try and abandon or a legitimate way to feel about it?