The basic reason behind Wendy and Peter wanting to get rid of their parents is that, being children, Wendy and Peter have already been given an unnecessarily significant amount of freedom. Once they blend their imagination, their heightened sensitivities, and the love for the freedom that they experience in the nursery room where they created the veldt, they begin to apply this need for freedom to their daily lives. However, when the parents become an obstacle to their freedom, the natural instinct of the children is to protect what they want and claim it. Hence, their imagination had already pre-conceived a world without their parents, where they could be free to do as they wish. For this reason, the wild animals in the mentally-transferred African veldt that the children built in the nursery room come to life and eat their parents.
The children had too many liberties for their age: they had the physical freedom to detach themselves from their parents and spend countless hours in the nursery room. They also had the psychological freedom to detach themselves from the real world, and create a brand new one, to their likings, which is how the veldt was created. The strong nature of a child's psyche and imagination, the story suggests, is the force behind the veldt's taking such a likeness to a real one. The angst of the children, their want for freedom, and the lack of parent support is what ultimately makes that same veldt to the impossible: it comes to life, and its wild animals kill the parents.