Wow, I'm a Libertarian, but even I see your argument as petty and weak.
By these sames standards, I assume you also consider it unfair that you might pay for health insurance when you're in good shape, car insurance when you've never had a wreck, public roads when you walk every where, schools when you have no kids, police protection when you live in a low-crime neighborhood, etc.
Here's a bit of a secret I'll let you in on. The days of being 100% self-sufficient are over. Humans realized long ago that societies are better for individuals. That way you don't have to spend every waking moment of your existence worrying about growing your own food, pumping your own water, teaching you own kids, protecting your belongings, performing your own medical care, creating your own forms of entertainment, writing you own books, birthing your own babies, etc.
In a society, you have people who can specialize and contribute in different ways to help other members. You can also have better things by pooling resources. And as long as you have that, you are going to have some that contribute more/less than others. It unavoidable. The best you can do it mitigate it as much as is reasonable and still benefit society, and thus individuals.
If this bothers you, feel free to move into the woods and live off the land. But don't come bumming around civilization when you need a tooth pulled or a wound stitched. I mean, why should people more learned/skilled offer to help you, the less fortunate?