In part one, Montag participates in a seemingly routine call, but when he arrives at the house, he discovers that the woman has not been arrested, and she refuses to leave her collection of books. Despite the fact that Montag and the other firemen pump kerosene onto the books and that Captain Beatty threatens to ignite the home with her inside, the woman is not deterred, refusing to leave. She then pulls out a match of her own and commits suicide by striking the match, which engulfs herself, the home, and the book collection in flames.
One could argue that the woman committed suicide because she felt that her life would be worthless without access to literature and knowledge. Bradbury's dystopian society is portrayed as a violent, empty society, where intellectuals and independent individuals live in constant fear. The woman more than likely feels that living in this superficial, ignorant society is not worth it and would rather die than survive and become a slave to society's interests and values.
Another argument could be that the woman feels empowered by becoming a martyr for the pursuit of knowledge and literature. If this is the case, she would rather commit suicide by lighting a match than allow Beatty the satisfaction of killing her.