Well, the root problem is the abuse that Marguerite suffered when she was living with her mother at the hands of her step-father. As Chapter 14 makes clear, the impact that this horrendous incident has on Marguerite is to make her hate herself which in turn makes her hate her life and robs her of any joy that she might have:
Sounds came to me dully, as if people were speaking through their handkerchiefs or with their hands over their mouths. Colours weren't true either, but rather a vague assortment of shaded pastels that indicated not so much colour as faded familiarities.
Mrs. Flowers speaks to Marguerite directly about the way that she won't speak in class or to anyone else. Marguerite seems to have closed in on herself like a flower who refuses to bud, and Mrs. Flowers directly addresses this issue, saying:
Now no one is oging to make you talk--possibly no one can. But bear in mind, language is man's way of communicating with his fellow man and it is language alone that separates him from the lower animals.
Thus it is that Mrs. Flowers challenges Marguerite's perception of herself and of others, and gradually fills her once again with self-respect and self-love through the simple process of spending time with Marguerite and letting her know that she is valued and esteemed.