The motif of betrayal
Each of the three main characters betrays the family. The mother has an affair, Jude destroys Noah's college application, and Noah hides Jude's best art from the family. As a motif, it seems to represent the implicit guilt people feel about their human nature, especially in the context of a family.
The duality of Jude and Noah
Although the two siblings are very similar objectively, they are different. Jude has permission to be flirty and fun. She's allowed to be attracted to men openly. Noah, on the other hand is condemned for his attraction to Brian. Jude gets to be tutored by a great artist after an education at art school. Noah gets almost nothing, except in the end when his relationship with Brian is redeemed.
The mother as a symbol of life
Each of the children has tension with the mother. Jude feels that the mother is a tyrant. Noah feels she is a hypocrite. Each of those opinions aligns with their respective opinions about life itself. Jude feels ashamed for her sexual nature, feeling that she is guilty for things that were out of her control, and Noah feels condemned for his homosexuality, even though the mother was having an affair, making her a hypocrite. In both cases, though, the mother dies, and each person realizes they have mis-allocated their frustrations. They're mad at life itself for being difficult and temporary.
The allegory of a gay man
Perhaps the novel could be understood as a reference to the unfolding psychology of a homosexual man. In comparison to his sister, he seems obviously preferable (he is the better artist at school, for instance), but he's secretly jealous of his sister. His sister show off her attraction to men, where Noah feels he must hide his attractions. Then, when Noah's mother dies, they are forced to reconcile their differences, and Noah finds what it takes to openly date Brian. He moved through jealousy, grief and ultimately fear, until he was eligible for the love life he'd always wanted.
The ghost of the tyrant mother
When Jude is at school, she feels constantly harassed by her mother's memory. She can't focus, she can't channel creative or artistic energy, so she's actually failing her classes. This doesn't change until she finally puts the issues to rest by telling her brother about all the secret guilt she's been carrying since the horrific accident.
