There are several themes at work in CODA. Seeing as the narrative aligns with the classic throughline of the hero's journey, a big one is Ruby claiming her independence by choosing to follow her life-path and not suppress her need by continuing to follow the path she has been leading, i.e., a key cog in the family's fishing business. Her own transformation, one of personal empowerment, is matched by the transformation of her family, in particular her mother, and even more specifically, her father.
That veers over into another theme: family. In another iteration of this story, the choir may have played a more prominent role as a kind of surrogate family, but in CODA, the group of singers really exists as a platform for Ruby to exhibit her personal growth. Her singing is more about her solo voice and the duet she rehearses and performs with Miles. While functioning as an Attractor character, Miles is not a prominent romance figure as he is someone to enable Ruby to express positive inner emotions and feel good about them. Their relationship also underscores her growing sense that the future offers possibilities for her she had not previously imagined. Another member of the choir "family" is Bernardo who, as a Mentor, represents an alternate father figure. The combination of Bernardo, Miles, and to a lesser extent the choir itself creates a parallel "family" for Ruby and, of course, generates conflict, both external and internal.
How does that conflict get resolved? I would argue the resolution points to the story's central them: Finding one's voice. The fact that Ruby trains as a vocalist and experiences some key vocal performances is a metaphor for her discovering and embracing her inner voice, the one that reflect her unconscious goal: to head off onto her own personal path, i.e., music school. Of course, the fact her father, mother, and brother are deaf lends this theme a unique flavor. Their inability to hear Ruby's singing voice makes Ruby's journey to independence that much more difficult. In fact, the parents, and in particular the father, have to quite literally see Ruby perform as a singer to finally grasp what music means to her, how it enlivens her, and how it brings her joy. So in a way, they don't so much as hear her voice as experience it visually. That adds to the distinctive way in which this central theme is explored and the primary conflict gets resolved.
Those are my thoughts, three key themes: Independence. Family. Voice. I'm sure there are more and welcome other opinions and analysis.
