In case you missed all the epigraphs throughout the novel, fire plays a huge thematic part of this story. Brian (a.k.a. Papa Fitzgerald) is a firefighter and his son, Jesse, is an arsonist. So they're both talking about fire from two different angles: starting them and putting them out.
The first part of the novel gives us a few revealing fire-related quotes like, "a fire will burn itself out, unless you open a window and give it fuel" (1.1.51), and "a fire can't burn forever. Eventually, it consumes itself" (1.4.7). By the time we get to Part 7, Jesse might as well be a fire—he's burning out of control, and one arson spree even almost kills a homeless person. So it's up to Brian to put out this fire that is his own son before Jesse consumes himself.
When Brian discovers that Jesse is the arsonist, he says, "I do what I know will destroy him: I pull Jesse into my arms as he sobs" (7.5.42). In other words, Brian smothers Jesse's fire as though Brian is the blanket squeezing all the oxygen out.
And it works. After that, Jesse reforms and Brian joins the police academy. Instead of committing crimes, he can now solve them. And importantly, he's on the same side as his dad now, so the tension from earlier in the book—the fire starter/fire fighter dynamic—is resolved.