What motivated the children to stay on the island despite its dangers?

The motivation for the children to stay on the island despite its dangers stems primarily from their belief that they were the last hope to save the world. Throughout "The Mysterious Benedict Society," the children grapple with significant challenges and risks, which are amplified by the dangers of the island. Their understanding of the gravity of the situation and their unique abilities instill in them a sense of purpose and responsibility. They recognize that their skills and teamwork are crucial in confronting the threats posed by the antagonists. This belief in their collective impact drives their determination to remain on the island, as they see their mission not just as a personal challenge but as a vital endeavor for the greater good.

Other motivations, like having nowhere else to go or a desire to explore, do not encapsulate the sense of agency and significance that the children feel regarding their role in saving the world. Similarly, while the children develop a bond with Mr. Benedict and may feel some allegiance to him, the larger motivating factor is their sense of duty to combat the evil they uncover.