The series of events that lead to Melinda and her father eating pizza for dinner showcases what Melinda sees as the shortcomings of her parents and their whole family. Melinda first explains why the dinner is important in the first place, particularly to her mother:

"Cooking Thanksgiving dinner means something to her. It's like a holy obligation, part of what makes her a wife and mother. My family doesn't talk much and we have nothing in common, but if my mother cooks a proper Thanksgiving dinner, it says we'll be a family for one more year. Kodak logic. Only in film commercials does stuff like that work" (pg 58)  

Clearly, Melinda is not convinced that a single holiday dinner will bridge the family's gaps in closeness and communication. Still, it is definitely depressing when her mother stays up all night working on the sales goals for the department store she manages and forgets to thaw the turkey. After that comes a series of emergency phone calls from Melinda's mom's department store paired with a series of failed attempts at quick thawing (hot bath, microwave, boiling). 

Then, Melinda's father steps in, taking the turkey into the back yard to try to break it into smaller, easier-to-thaw pieces with his hatchet. It is a total failure, and Melinda's mom takes off to deal with the emergencies at her store. Melinda's dad takes over, saying:

"Just like the old days, right, Mellie? Fellow goes out into the woods and brings home dinner. This isn't so difficult" (pg 60).

Just like Melinda's mother tried to be the perfect homemaker with her dinner, Melinda's father tries to be a sort of macho frontiersman. He is no more successful than she was.

In the end, "[Melinda] order[s] double cheese double mushroom. Dad buries the soup in the back yard next to our dead beagle, Ariel" (pg 61). The fact that Melinda brings the turkey carcass to art class and creates a piece depicting a girl trapped by the family tradition shows that the disastrous Thanksgiving is emblematic of the family's larger issues.