Preparing to confront the father
The most subtle theme in the novel is the way many of the novel's events are secretly practice for Holling. Holling will need certain skills in order to navigate the unreasonable, aggressive expectations of his father, like a certain capacity for language (which he learns by reading Shakespearean drama), or like sincerity. Sincerity is a harder skill to cultivate, but Holling decides to date Meryl Lee, knowing his father won't approve (because their dads work for competing companies). These are all skills that will help Holling to navigate the difficult confrontations he must have with his father in the fullness of time.
The function of religion
The reader should view Holling's relationship to Mrs. Baker as inherently religious, because after all, he is alone with her, which is unusual in any case, but also because his time with Mrs. Baker is during "Church Class" time when the rest of the school goes off for Catholic or Jewish midweek classes. In other words, because Holling isn't like the rest of the kids, Mrs. Baker ends up being his religious instructor in a roundabout, unspoken way. Instead of teaching him theology, she teaches him about literature, but the effect is similar.
Vietnam, and broader social issues
Part of Holling's religious instruction is that he is asked to consider that his teacher, Mrs. Baker, has a husband who is fighting in the Vietnam War. He must reconsider her as a person, because he never knew she was up against so much stress and tragedy in her day-to-day life. In other words, the war in Vietnam serves as a thematic reminder to Holling that if he wants to be successful in life, he will need to think more broadly about human suffering, because even though he can't see it, many, many people in his community are secretly grieving the war.
