Jack is insecure, but in the way that typically manifests in people. He exerts confidence: he promotes his work, praises it, and assures that his work is good. This confidence goes deeper than a mere projection; he actually believes that his work is good and believes, among other things, that he’s well-liked and handsome, thus it is easy to assume that he has no insecurities-assumptions that are based on observations what he projects to be of importance to him, namely his writing. In this way Jack is a master of misdirection.
He does have insecurities, or he has a insecurity that’s unknown to all but his family. Jack wants to be a war hero. He wants to be like his father, the famed General Driscoll. Regardless how complex and hard-hitting his plays may be, Jack never feels as if his words are enough to leave a great impact on the world. He wants to fight for some great ideal. He wants to protect people, to save the life of an innocent, to command an army, to be great just like his father. That he was too young to join the army during World War I, that he wound up a writer instead of a soldier, that he hasn’t done any of the great things his father has done in combat, is the source of his greatest insecurity. As people are tricked into believing that Jack’s only passion lies in theater, this insecurity goes unchecked.
His father knows it well because Jack has made a number of self-depreciating comments around him, saying that what he writes does not compare to what his father did. His father thinks he’s being foolish, but he can’t seem to get through to Jack. Since this insecurity has remained unchecked and largely unknown by people who can snap him out of it, it has caused him to do things that might seem out of character for a writer like him-like risking his life to save Ann from a 25 foot ape.
This insecurity might grow into a huge problem. I’m not sure yet, but I do worry about the boy, and I'm worried his fear of being a failure will spread into other things--like his romantic life.
ETA: Note on romantic desires:
I think what he wants more than anything is a woman who makes him feel worthy.