In Tolstoy's initial conception of the novel, Anna was portrayed as an unattractive woman, designed to arouse the dislike of readers. That's obviously not the Anna we see in Anna Karenina. Were you rooting for Anna? We were. How could we help it? Anna's entrance into the novel is compelling and dramatic. We hear about her in the Chapter 2, when Oblonsky and his valet hail her as the potential savior of the Oblonsky household, but we don't see her until Chapter 18. This is a dramatic build-up, and when we are finally introduced to her, we're not disappointed. She is beautiful, charming, and vivacious. She reconciles Oblonsky and Dolly to each other. The children, Kitty, Dolly, Vronsky – everyone falls for her, and we fall with them.
When Anna returns to her husband, it becomes clear that Karenin's "unromantic appearance" is very unromantic indeed. Compared to the handsome Count Vronsky, who we just saw making a passionate declaration of love, Karenin is a cold fish. Later we see a snippet of ordinary life in the Karenin household, and although everything seems perfectly fine, it's clear that something is missing. Anna struggles to find this missing piece, but by the end of the book she is unrecognizable from the woman with whom we fell in love.
On the surface she is as beautiful and charming as ever, but instead of being natural qualities, they are imbued with sad desperation. She has fallen from grace. Society shuns her. Kitty blushes when they meet. Unable to face the reality of her situation, Anna takes morphine to help her sleep. At the end of her life she is demanding, frantic, and paranoid. Her transformation is arguably the most compelling story in the novel, and undoubtedly gives her the title of "protagonist." If that doesn't convince you, remember that the novel is named after her.
Maybe we’re not in love with Levin the same way we are with Anna, but he is still a protagonist. His personal journey throughout the novel is the most intense of any of the characters, even – arguably – more intense than Anna's. This alone demands that he be recognized as a central character. At the same time, however, his particular storyline acts as a foil to Anna's storyline. As Anna breaks off relations with her husband, Levin commits to marriage with Kitty. Anna questions the meaning of life, deciding ultimately that we are all meant to suffer, and throws herself under a train. Levin also questions the meaning of life and entertains thoughts of suicide before deciding that life holds the meaning that he puts into it. In so doing, he achieves a crucial spiritual peace.