I often enjoy doing things on my own. Yes, in some ways it increases my confidence. I never liked relying on other people for anything, always liked the feeling of being independent.
Some of my best vacations have been windsurfing trips I've taken by myself. Sailing is a great sport for loners, you can go by yourself --lots of people do-- but there are always other people around to talk to if you feel like it, and lots to talk about, even with strangers, because everyone there is into the same thing.
Like becks said, it is fun to share moments with others, but having the confidence to enjoy things on your own is really pretty special, something that lots of "normal" people don't have.
"To study the Way is to study the self. To study the self is to forget the self. To forget the self is to be enlightened by all things. To be enlightened by all things is to remove the barriers between one's self and others."