Why does Holden not want Phoebe to come with him out west at the end of The Catcher in the Rye?

Holden doesn't want Phoebe to come out west with him because he realizes he is putting his fantasy need for escape ahead of her real needs to live her life as a healthy, well-balanced child. He remembers how very excited she was, when he visited her at home, to tell him about her role playing Benedict Arnold in her school play. Holden knows she is brimming over with excitement about acting this part and that she wants him to come see her in it. He knows that if he runs off, even taking her with him, that he is being no different from her father, who can't come to see the play because of his own priorities—and no better than a Benedict Arnold himself, betraying her. He realizes that she needs, overall, to be in school. He is selfish if he takes her away or allows her to sacrifice her needs to his needs. He says to her, being uncharacteristically harsh

"I thought you were supposed to be in a play at school and all I thought you were supposed to be Benedict Arnold in that play and all," I said. I said it very nasty. "Whuddaya want to do? Not be in the play, for God's sake?" That made her cry even harder. I was glad. All of a sudden I wanted her to cry till her eyes practically dropped out. I almost hated her. I think I hated her most because she wouldn't be in that play any more if she went away with me.

He thinks that he would hate her because she wouldn't be herself if she ran away—but primarily, he means he would hate himself. He realizes he is dragging her into his spiral of self-destruction. He comes to his senses and tells her that he is taking her back to school and that he is not running away. He is behaving like a responsible adult here, not like a self-centered adolescent, showing he is growing up.

The Catcher in the Rye is a bildungsroman novel by J.D. Salinger. Holden Caulfield, the protagonist, provides one reason regarding his decision for not wanting Phoebe to come with him out west. Holden openly states that he does not want her to go with him because, if she did, she would not be able to be Benedict Arnold in a play at school.
As the chapter (25) continues, Holden tells both readers and Phoebe that he changed his mind. He is not going to leave—he is going home. Essentially, he cannot face Phoebe hating him or feeling abandoned by him. When he takes Phoebe to ride on the "carrousel," he refuses to ride with her. Phoebe asks him numerous times, yet he only wants to watch her. It seems, in the end, that Holden has found his calling in life: to take care of his sister. If he were to leave, he would not be able to make sure Phoebe lived a happy life. He simply cannot bring himself to leave her alone—he wants her to live a life far different from the one he lived/lives. He does not leave, so he can take care of his sister.