I get this. I never want company until I'm alone for a little while, then I get lonely. But if I seek out people, I grow frustrated with them quickly and long for solitude. Even when I'm engaged in a solo activity I feel better with other people in the room, but sparks fly if they interrupt me.
It's worse when I'm feeling paranoid. Then I want to avoid people because they might be spying on me, but if I'm not around I worry that they'll talk about me.