There's no one person who's really fighting against Claudia and Jamie, but there's something, for sure—boredom. The two siblings are smart, curious kids who want to learn everything and go on great adventures, but they're held down by their humdrum day-to-day lives. They have to go to school, do chores, collect allowance, and take turns looking after their bratty younger brother. Why did they run away?
A reason that had to do with the sameness of each and every week. […] She was tired of arguing about whose turn it was to choose the Sunday night seven-thirty television show, of injustice, and of the monotony of everything. (1.4)
By running away, Claudia and Jamie get to escape all of that stuff. They make their own schedules and can learn and do whatever they want. They don't have to do what adults or schools tell them to do. They can explore as much about Egypt and Renaissance Art as they want, and no one's going to tell them that they're too young to do it, or that it doesn't fit into the right schedule.