Most of the main characters in Giovanni's Room are terrified of being alone. They are constantly rushing into one another's arms, looking for company. Yet, the desperate nature of their relationships tends to only increase their loneliness, and it is difficult for any of them to find a way out. What becomes clear as the novel goes on is that lies and deception lead to isolation, and that only honesty can bind people together.
The fact that David and Giovanni try to hide their loneliness from one another means that they cannot have an honest connection, and the result is that their loneliness only increases.
Though David seems to be afraid of being alone, he often appears most isolated when he is involved with other people.