Why does it take Tom so long to decide to leave home?
Tom clearly wants to leave home. He is very unhappy, and feels, understandably, that he is being stifled in the household:
I’m starting to boil inside. I know I seem dreamy, but inside—well, I’m boiling! Whenever I pick up a shoe, I shudder a little thinking how short life is and what I am doing!—Whatever that means, I know it doesn’t mean shoes—except as something to wear on a traveler’s feet! [Finds paper.] Look—
At the same time, Tom seems to feel some responsibility to his family, especially to his sister Laura, and no sooner does he leave the apartment for the last time than he begins to feel guilty for doing so. He is extraordinarily frustrated, but the end of the play makes it clear that a sense of obligation, and and perhaps a desire not to be like his father, whose departure has left him in this mess, that keeps him at home as long as he is.