There's nothing wrong with being single... it's just that the inclination to be with someone is a very strong, instinctual drive. We're social creatures... thrive best with others than we do in complete isolation... and have a desire to mate -- strike that, a strong desire to feel really, really good that may lead to mating (especially if you forgot your contraceptive or you actually believed her when when she said she was on the pill).
If being independent is what you desire, then go for it... and don't care what others think. Do what makes you feel comfortable.
"The weakest soul, knowing its own weakness, and believing this truth that strength can only be developed by effort and practice, will, thus believing, at once begin to exert itself, and, adding effort to effort, patience to patience, and strength to strength, will never cease to develop, and will at last grow divinely strong."
- James Allen