Junior's father and Junior's new friend Penelope both have an unhealthy way of dealing with their pain. While his father turns to alcohol to deal with the hardships of life on the Reservation, Penelope has developed bulimia as a way of assuming control over at least one facet of her life.
Upon learning about Penelope's bulimia, Junior tells her not to give up, which is the same advice he repeatedly gives his father when he is drunk. The connection between alcoholism and eating disorders is immediately obvious to Junior, who understands that both are addictive behaviors; both are a way of escaping pain and both are potentially deadly.
Junior has his own coping mechanism, which is drawing cartoons. The only difference is that his coping mechanism is harmless, unlike eating disorders and alcoholism.
The analogy that Junior discovers between Penelope and his father is based on the particularly damaging behaviours that both of them engage in. This is when he discovers that Penelope is bulimic and she attempts to explain to Junior why that is better than being an anorexic, but she is only a bulimic when she is actually being sick, whereas, in her opinion, anorexics are anorexic all the time. This creates a moment of insight for Junior, as he realises that everybody is alike, even somebody like Penelope and somebody like his father, as everybody has pain and everybody tries different ways to make it vanish:
Penelope gorges on her pain and then throws it up and flushes it away. My dad drinks his pain away.
This is a significant moment for Junior, as it marks his realisation that even though one of the biggest defining differences in his life is the colour of his skin and his ethnicity, there are actually things that unite all humans, no matter whether they are Indian or white.