Alone Not Lonely
Kurama was alone, but he wasn't lonely. He had all his friends and of course he had his mother and that's all he needed. To be honest he didn't want anyone else. His mother had taught him the emotion the Ningens called love and he was alright with it. That type of love satisfied him. He didn't desire romantic love; in fact romantic love was the one thing he didn't understand. That's because he never had the opportunity to study it. That chance had been taken from him or more precisely he took it from himself.
Maya
This human girl made him feel things he had never felt before. These feelings might have been something akin to love, he wasn't really sure, as a demon he didn't know what love we and as a human the only love he knew was for his mother and that only came years after he entered Living world.
The feelings he felt for Maya both delighted and frightened him. Maya scared him with her feelings. She depended on him and he couldn't let her down, but he did and she was taken. He saved her, of course, he had no other choice but then he had to do something he hated doing.
He had no other choice, he erased her memory and when those memories faded so did her feelings for him. He had never felt sad before but he did at that moment. It was then he decided never again would he let foolish emotions like love to control him. He never wanted to be broken hearted again. That's why he never gave in to one of his many fan girls. That is why he never sought love.
He would be alone, but he would never be lonely.