JAAY, I don't think there are normal friendships. We say normal, but that's a relativistic term. What is quite normal to one can be abnormal to another. I'm not saying individual relativism is the correct way of seeing things, but neither is adopting the majority viewpoint. A lot of people have what we call friends and because I don't share that characteristic with them I'm supposed to be strange and different? I don't think so.
The problem is we don't know what is being meant by the word friends or even by normal so we may be talking about totally different things. Friends to one person can be someone who simply listens and is always there to comfort when they need it. To another, friends can be the people we spend our free time with. Clarification is sometimes required yet most people don't even bother to think about those type of things. They just haphazardly assume they know what is being said.
I guess I'm not entirely sure what normal friendships are. I have pushed most if not all people out of my life and for as long as I can remember, I've never desired to be physically around non-family. Most of what I consider to be friends are online anyway.
I can get along with others for a while but then it's like they know too much or I feel they aren't being sincere. I get paranoid so I withdraw and then I let them go without even saying as much as a good-bye. This is one reason why I've been diagnosed schizotypal. The other reasons are for what are considered to be odd and eccentric ways of thinking. For example, I use to consider myself to be pagan, then Christian, then atheist, then freethinker, then agnostic, then Gnostic, now I don't consider myself anything at all because in a way I am all those. (reminds me of the Hegelian dialectic) How many normal people do that? I don't try even making sense of it anymore. Like the burning bush said to Moses: I am that I am.
Jesse