Jem comment ignites Scout's anger because she is sick of Jem acting superior.
Explanation:
Jem, who is four years older, has been speaking to Scout in a didactic tone as of late, instead of his typical friendly manner. When Jem threatens to spank Scout, she grabs his hair and punches him in the face, and fighting ensues.
The main idea of I Am Malala is the importance of world peace and girls' rights to education, as well as the willingness of one brave girl to fight for these ideals.