I don't think that's really nihilism but more of a social phobia? If we're talking about people. Why don't you want to attach yourself? Are you afraid of losing whatever you are attached to? I think there's a difference between being attached to something and giving a lot of importance in your life and being obsessed with something. If you're obsessed, when you lose that thing, your entire life seems to be incomplete. Attaching yourself to things means that you can let them go if need be and will just move on to something else.
I don't like attaching myself to things or ppl that much nowadays either, something about fearing abandonment. And sometimes I make the first move in abandoning, that way, I feel in control.