OP, I completely relate to this. My entire life has been a series of just wanting/having one friend at a time - I seem to be incapable of being attached to more than one person at a time. No one else is important if I have one friend I really like. Why would I need any other friends when I have this one person? I actually still can't understand why someone would need more than one friend at a time, and the thought of actually having and maintaining more than one at a time blows my mind.
It makes sense to me personally, if I can only focus on one thing at a time in other regions of my life, it's not surprising to me it holds true socially.
The only problem happens when the friendship with these people changes or passes for whatever reason, and then there's no one, and it's just uncertain waiting for the next one. For me it's very frustrating as well since like other interests, I am extremely particular about the people I am able to be interested in/find important, and they are extremely rare. Sometimes I wish I could like/get along with a broader range of people, but other times I remember I'm better off without trying to deal with them.
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'No one designed us. We're just an accident, Harold. We're just bad code.'