Throughout the seven Harry Potter novels, Harry and Malfoy engage in what is one of the most famous rivalries in young adult literature. Early on in Harry Potter and the Sorcerer's Stone, Harry meets Malfoy aboard the Hogwarts Express. Initially impressed by Harry's fame, and seeing that Harry has become friends with Ron Weasley (who comes from a poor family), he offers friendship to Harry. He says,

You’ll soon find out some wizarding families are much better than others, Potter. You don’t want to go making friends with the wrong sort. I can help you there.

Harry rejects this hateful idea that Malfoy presses upon him. Harry has already made close friends with Ron, whom he likes and respects, and is upset at the idea of someone claiming his newly acquired friend is inferior.

Part of the reason for their rivalry is Malfoy's intense arrogance and jealousy of Harry's fame. Malfoy, a self-proclaimed wizard at Quidditch, is revealed to have comparable, but not superior, skills to Harry's.

Ron says of Malfoy's Quidditch skills,

Anyway, I know Malfoy’s always going on about how good he is at Quidditch, but I bet it’s all talk.

Once Gryffindor defeats Slytherin in a Quidditch match, it becomes clear that Harry and Malfoy's rivalry will only continue. Malfoy vows revenge, confident that his skills are still greater than Harry's. Malfoy's arrogance, pretentiousness, classism, and general nastiness repeatedly repulse Harry, who prefers to be in good company.