Rough Around the Edges
Sandy and Danny are loveable, but they're like a white bread sandwich. And by that, we mean a piece of white bread between two other pieces of white bread. No butter. Untoasted. Hardly any flavor.
Compared to this bland snack, Betty Rizzo is like blue cheese. Not everyone likes her, but everyone who does loves her.
When we first see Sandy and Danny, they're pledging their pure love for one another. Rizzo makes a different entrance, announcing this:
RIZZO: We are going to rule the school.
And how is she going to do that? By drinking, smoking, swearing, and having sex, that's how. Rizzo is in a group of girls like her—Jan, Marty, and Frenchy—and they call themselves the Pink Ladies. Rizzo appears to be the gatekeeper, because Frenchy has to ask permission for Sandy to join them. What does Rizzo say?
RIZZO: She looks too pure to be pink.
Not Betty White, But Betty Pink
Even though Sandy never says she wants to even be a Pink Lady, Rizzo appears to be trying to change her throughout the movie. She convinces Sandy to drink and smoke and makes fun of her for being "pure." Why does Rizzo treat Sandy this way?
Rizzo clearly chooses to act the way she does, as we witness in her solo, "There are Worse Things I Could Do." Perhaps Rizzo used to be like Sandy, but wasn't finding happiness, so she decided to do a complete one-eighty, going to the other extreme of the behavior spectrum.
This isn't as ridiculous as it might seem. Pay attention to the scene where Rizzo wants Kenickie to call her by her real name: it's Betty. She has the most generically wholesome name of the time. She may be railing against this whole Betty image by trying to be a bad girl.
If so, maybe she is jealous of Sandy for living a "pure" life and actually finding happiness. Sandy actually calls Rizzo out on her in the following exchange:
SANDY: You're making fun of me, Rizz?
RIZZO: Some people are so touchy.
Rizzo acts big and bold, but she can't even admit to Sandy's face that yes, she's making fun of her. To do so, would be like admitting she's making fun of herself.
Why else would someone who acts so independent constantly peer pressure another to act just like her? She could be jealous of Sandy's relationship with Danny Zuko. Or maybe she just thinks Sandy would look really good in leather.
Rizzo's extreme attitude—Xtreme Riz, we'll call it—gets her in trouble. And by "in trouble" we don't mean, "stand in the corner and think about what you've done." We mean "stand in the corner for nine months, then give birth, and take responsibility for a child you got pregnant with by accident."
About halfway through the movie, Rizzo ditches the slumber party for the following reason:
RIZZO: I'm gonna get my kicks while I'm still young enough to get 'em.
Getting pregnant forces a girl to grow up fast. Rizzo's commitment to her fearless identity leads her to make a careless mistake.
Much to Rizzo's chagrin, the person she hates the most steps up to help: Sandy. In a brief scene, Sandy tells Rizzo she'll help any way she can. Some fans speculate that Sandy helps Rizzo pay for an abortion. (Source) But whether Rizzo simply missed a period, had a miscarriage, or had an abortion, one thing's for sure: Sandy's kindness makes Rizzo realize that she needs to be a little more like Sandy to be happy.
Rizzo takes a page from Sandy's Big Book of Forgiveness and makes good with Kenickie at the end. They live happily ever after…or at least until the credits roll.