The relationship between Alec and the Black grows and deepens throughout the story. In fact, you could consider that it is at the heart of The Black Stallion as a novel. While you could choose several quotes to fit your specifications, here are a few of my favorites.
Slowly the boy walked toward the Black. The stallion's mane swept in the wind, his muscles twitched, his eyes moved restlessly, but he stood his ground as the boy approached. Alec wanted the horse to know that he would not hurt him. Cautiously he reached a hand toward the stallion's head. The Black drew it back as far as he could without moving. Alec stepped closer and to the side of him. Gently he touched him for an instant (26).
This quote illustrates Alec's patience and the Black's nervous nature. They start out here, mutually dependent on one another yet wary. It is from this base that they gradually begin to build a trusting relationship.
By page 32, everything has changed:
With the days that followed, Alec's mastery over the Black grew greater and greater. He could do almost anything with him. The savage fury of the unbroken stallion disappeared when he saw the boy.
Here, we see that Alec has earned the trust of the stallion. The text refers to his mastery, which will become important as the two move on in the story and become a team. Alec and his horse work together and respond to one another, beyond what a typical human-equine team might do. More than that, the Black will not tolerate any other rider. That is why this quote is important.
Jim Neville, the newspaper man, recognizes this. He is the one who organizes the Black’s race, in which he demonstrates his excellence by beating two champion racehorses. When seeing Alec and the Black ride together for the first time, he says, “Kid, I’ve seen a lot of riding in my day, but never any to equal that!” (136). Later, once the race is set, he says, “Boy, I’ve gone way out on a limb with him. Got to wondering whether I’d been dreaming about that night…” Jim, even though he has seen many horses, still finds something special in the Black and Alec. The reporter takes his horse’s side, even when others doubt. When they arrive in Chicago, he proudly says “We’ve a horse here—for the race tomorrow.” The mystery horse is the Black, who will soon leave the two former winners in the dust.