I read the book a long time ago but here’s my best answer:
The competing notions of what a utopian society should look like lead to conflict in Fahrenheit 451. The governments idea of a perfect society is one where they are in complete control, and individuals can not express personal freedoms. However inevitably you can not design “a perfect society" for an imperfect species. So naturally a struggle arises between the main character, Montag, who believes in the freedom of self expression, and the government. It is this clash of ideology’s that causes all conflict. Ultimately it this leads to death, destruction, and chaos through the novel.
Hope this helped :)