In Brave New World, why is the Director is leading the students through the Hatchery?
There are at least two levels on which one can answer this question.
First, on the literal level, the Director is leading the students through the Hatchery so that they can get an overview of the process of creating new life in this society. He tells them that this is their one chance to get a sort of overview of the general proces. After that, they will be involved in the details of their training.
Second, though, we need to look at why Huxley would have this as the first scene of the book. I would argue that he does so to give us a quick (and somewhat shocking) view of how different this "brave new world" really is. As the Director leads the students through the Hatchery, we learn about how there is no longer natural reproduction. We learn how proud they are of their scientific ability to totally remake the world. We learn that the whole point of their society is to create stability. All of these things are important things to know about this society. By starting the book with this tour, Huxley introduces us to these very basic and important facts about the society in this world.