Clearly, the major instigating incident that leads the children to take such terrible revenge on their parents comes when George and Lydia feel that their children have been spending too much time in the nursery and have become fixated on the African veldt and the dangers of hungry lions. Yet, if you read the text carefully, the parents note that their children have been behaving "strangely" ever since they had been forbidden to take a rocket with them to New York. As Lydia comments, "They've been decidedly cool toward us since."
Bradbury paints a picture of a world that is terrifyingly real and where the children are given everything. As the parents comment when they think about what they did wrong:
"We've given the children everything they ever wanted. Is this our reward--secrecy, disobedience?"
"Who was it said, 'Children are carpets, they should be stepped on occasionally'? We've never lifted a hand. They're insufferable--let's admit it. They come and go when they like; they treat us as if we were offspring. They're spoiled and we're spoiled."
So, whilst we can see that the inciting incident involves the parents trying to assert their authority on the children and preventing them from engaging in harmful activities, we can see that the real damage was done much earlier, when the children and the adults were born up in a society where they never had to do anything, and were "spoiled" as a result.