Asagai believes that Beneatha's hairstyle and even her career goal demonstratethat she is assimilating into "white" culture and giving up her African heritage. Her choice to straighten her hair--in Asagai's view--means that she is unhappy with her natural African features and that she wants to look like "everybody else." Beneatha's desire to be a doctor is not at first connected to helping people in Africa; so he views her goal as trying to prove to the white man that she is just as intelligent as he is.
In fairness to Beneatha, she was born and raised in America; so one could argue that she is simply expressing her American roots through her hair and career goal. Asagai would have difficulty seeing her choices as American and not as trying to be white because he is from Africa and has a very opinionated view of what it means to be black. Nonetheless, Asagai's influence on Beneatha is powerful, and once she decides to be more "natural," she is happier with herself and more stable in her decision-making.