Why does Shasta leave his home in search of Narnia in The Horse and His Boy?
Shasta leaves his home to search for Narnia because a stranger is bargaining to buy him from the man he calls his father. He is afraid of what this stranger might be like, so when he is invited by the visitor's horse to run away to Narnia with him, he takes the opportunity and flees his home in the southern land of Calormen.
As long as he can remember, Shasta has lived with the fisherman Arsheesh. Shasta is fair, completely unlike the other people in the area who are dark, and it is obvious he is not Arsheesh's real son. In truth, Arsheesh shows no love for Shasta, and treats him like a slave. When the stranger comes, Shasta overhears him talking with Arsheesh and learns that Arsheesh had in fact found Shasta as an infant, in a boat on the beach, with a man who was dead. It is a relief to Shasta to know that he is no relation to Arsheesh.
Shasta wonders what kind of man the stranger is, and if he might not be better off with him. While he is pondering the matter, he wanders over to where the stranger's horse is tethered. To his surprise, the horse, whose name is Bree, talks to him. Bree is from Narnia in the north, where the people are fair like Shasta and "nearly all the animals talk".
Bree tells Shasta that the stranger is a bad man, and that he'd "better be lying dead tonight than go to be a human slave in his house tomorrow". Shasta decides that, if what the horse says is true, he'd do well to run away. The horse himself was kidnapped from Narnia when he was a foal, and would also like to escape and return to the land of his birth. Bree points out that the two of them need each other; if the horse were to go without a rider, anyone who might see him would be after him as a stray horse, and Shasta, with his "two silly legs...what absurd legs humans have!", would be able to travel much more quickly atop a horse. The two decide to take advantage of the situation, concluding that "this is the chance for both of (them)" (Chapter 1).