We chose not to bring Jean because Jean is a young baby. A baby is not a good candidate to be on a stranded island because they do nothing to contribute to the situation. In fact, they cause nothing but trouble because it is a distraction to everyone on the island trying to work together to survive because a baby needs to be cared for. A baby requires around the clock care, and no one is around to care for such a young child.
In addition because there is so little recourses on the island, there is a slim chance of survival for such a young and vulnerable child.