Neglectful parenting
Mayzie is a symbol for a neglectful parent. She clearly does not want to take responsibility for her children and manipulates Horton into taking care of her nest whilst she takes a holiday.
Parental role
Horton is the definition of a solid parent throughout the book. Despite not being their biological parent, he happily assumes this role and cares for the nest for the duration of Mayzie's leave. Indeed, he puts up with a lot of personal risk from the poachers but still refuses to leave them, highlighting the strength of his love for the nest.
The Nest
The nest is a symbolism for something that people should dear to their hearts. In the story the nest is something Horton comes to care for but young readers can interpret the nest as being something in their own lives that they hold previous.
