Any good story, no matter the genre or length, needs a dynamic lead character; that is, they will transform as a person and end the story as a very different character than when they started. Conversely, a static character will learn no lessons or skills, make no meaningful friendships and have the same worldview or place in the world.
Soma Yukihira may be the hero of Food Wars!, but he's a static character who's only really changed in regards his cooking skills. In all the ways that count, Erina Nakiri is the true hero, and her personal arc proves it.
The Lofty Queen
To illustrate Erina Nakiri's personal growth as a proper protagonist, it's important to cover where she's coming from, and what sort of girl she used to be. From the moment of her birth, Erina was special: she's a Nakiri with the God Tongue, meaning she has better taste buds than anyone on the planet. Her family is a prominent one in Japan, and she was raised in opulence and with many admirers. This made Erina rather uptight and spoiled, though she did have a reasonably good relationship with her cousin, Alice Nakiri.
All that changed when Erina's father Azami took a more direct role in Erina's upbringing. He taught her to become the ultimate food critic, to only accept the pinnacle of cuisine and to reject the rest as "pig slop" or peasant food. Erina was a goddess, Azami believed, and she had no place among commoners. Erina feared and resented this paradigm, but she did internalize it a great deal, and entered Totsuki believing that she was the best of the best. She sneered at Soma and doubted his abilities, and she openly awaited the day Soma would prove himself a failure and wash out. Despite it all, Soma persisted, and Erina began to change her tune.
The Real Erina Nakiri
Erina was often critical of Soma, but also gave him fair evaluations of his abilities, giving him chance to prove himself. Qhen Azami arrived, everything turned upside down. Azami wanted to take Erina back, and Erina was frozen with terror. But Soma, Alice, Ryo, Hisako Arato and her other associates smuggled her into the Polar Star dorm, and Erina's true transformation began. She realized, bit by bit, that her role as the world's greatest food critic was something she had to earn, and her future was hers to mold into shape, not her father's. She accepted her role as a rebel chef and led the other rebel students, openly defying her father and his Central administration.
At this point, Erina realized she is her own person, and nothing can take that away. She became Soma's partner and friend, and her distant relationship with Alice was bridged. As Erina fought Central's chefs, she began to fight with Soma's style: unpredictable, unorthodox food served with a "happy to serve you!" at the end. This level of personal expression was new to Erina, and she reveled in it. She even became Totsuki's new dean, to repalce her grandfather and run the school her own way. Later, she cooked to impress her own mother, Mana Nakiri, in the BLUE competition and started to doubt herself once again. Until, that is, Soma fired up her competitive spirit once again, and she cooked with renewed passion and faith in herself. And she never looked back.
Erina transformed herself from a lofty but insecure girl to a free, independent, and loving young woman who's ready to shape her own future. This is the exact sort of story a good shonen protagonist should have.