There is a difference between being alone and wanting to be left alone.

 Being alone is a feeling of dread, where there is nobody that cares about you. It is when you are down and have no one to bring you up. 

Wanting to be left alone is when you are having an issue and want it to stop. You don’t actually want to be alone, you just want to be free from the issues. 

Even when you say “i want to be alone”, you don’t. Nobody actually wants that. Without someone to be there at your side, you will deteriorate. Both physically and mentally, you will shut down. You will lose a part of yourself that you will forever want back. 

Nobody wants to be alone. They just want the pain to end.