There could hardly be a world for me without Anne, there was hardly world enough for us both. (2.9)
Mary and Anne have a symbiotic relationship. Their drive to compete with one another is what keeps them going.
"You can simper at your husband all you like, Mary. When I marry I shall do better than you by far." (4.107)
Anne sees everything as a competition. She even turns getting married into a race of who can marry better than the other. Of course, no one behaves like this anymore, because we know marriage isn't a competition…Oh, wait.
"I was born to be your rival," she said simply. "And you mine. We're sisters, aren't we?" (13.67)
Some sisters steal clothes or toys. Anne Boleyn steals husbands. Because Anne and Mary are members of a scheming, power-hungry political family, their normal sibling rivalry is upped a thousand times; the stakes are really high.
"You're accursed, Anne, you lost your one love and now you want anything that's not yours. You want anything that's mine. You've always wanted anything that was mine." (14.348)
Anne always wants what she can't have. As a woman, that means she wants power and independence more than anything else, and she'll take down her own sister in order to get what she wants. On the other hand, her extreme behavior is part of her downfall. Sure one of the things we see is that women are punished for things men take for granted—like having power—but it's also true that Anne is as nasty and scheming as the worst of the men, so what comes to her isn't totally a surprise.
I curtsied with a sweet smile to Anne. "I am the favorite," I repeated. "And she is to disappear." (15.35)
As much as Mary hates Anne's competitive nature, Mary isn't above gloating when she triumphs over her sister.
I gave a little triumphant laugh. "Because you're older every day," I said spitefully. "And so is the king. Who knows that you can make a child at all? […] You'll never have a boy like my Henry, Anne. You know in your very bones that you'll never have a boy to match him. All you can do is steal my son because you know you'll never have your own." (22.86)
Mary can seem mean at times, but she's never as mean as Anne is. These two come from the same family, so it's maybe not such a surprise that each of them has a mean streak. After reading everything Anne does to Mary, we feel that she deserves to be told off—and that she's getting off easy here.
"She takes everything," I said. "She has always taken everything. But I will never forgive her this." (22.92)
Anne crosses the line when she takes Mary's son as a pawn in her game for the throne. To Mary, that's not playing fair. We mean, to anyone, that's not playing fair. But Anne uses whatever weapons are available to her.
"She is Mary, the other Boleyn girl. And I am Anne, Queen Anne to be. There is a world of difference between us two. We don't share a name. She is next to nobody and I will be queen." (32.67)
Anne gloats, too. She's probably been waiting for this moment since Chapter 22, when Mary bragged about her own triumph over Anne. On the other hand, the very things that make Anne succeed where Mary failed (in becoming queen) are the things that will take Anne down in the end, whereas Mary gets to lived happily ever after, at least in comparison.
"If I have to become Jane Seymour myself, I might as well be set aside." (47.624)
Anne knows she would lose in a game of "Who is more virtuous?". She would be about as bad at that as Kim Kardashian would be at winning a modesty and humility pageant.
There was too much to send in one message. There were long years of rivalry and then a forced unity and always and ever, underpinning our love for each other, our sense that the other must be bested. (49.131)
Mary acknowledges that she and Anne were rivals first and sisters second. But to her, the complexity of their relationship strengthened their bond with each other. Do you think she's right? How does this play out throughout the novel?