Is this bad or unnatural?

There's nothing wrong with having a different set of personal space. You aren't obligated to let people touch you whenever they want.

No, it is not bad or unnatural at all, Some people don't like the feel of being touched. But also don’t let yourself get too busy that you starve yourself of touch. It’s important for your physical, mental and emotional well being to touch others and let others touch you, on the same note you are in charge of your own body and nobody can tell you that you HAVE to let them touch you. You have the voice that can or can't allow any form of touch! Don't feel bad about it. It is just who you are and there is nothing wrong with that!

There's nothing "bad" about not enjoying hugs. You have a right to your personal space. It sounds like you only feel comfortable with touch when it's coming from someone that you're close with, and there's nothing wrong with or weird about that. If someone that you are not comfortable with tries to hug you, try politely explaining that you're not a touchy person, and try replacing hugs with something you are comfortable with, like a high five or fist bump.

I don't like to be touched either... I tend to just bare it, but I hate it.

There is no need to feel bad about that I had the same thing in hs, now I'm a happily engaged person

that's totally fine, not everyone likes physical contact. maybe try to explain that you don't really like showing affection physically with anyone, but that doesn't mean you don't like them.