Bree developed a very high opinion of himself with only non-talking horses to compare himself to, further enhanced by his status as the prized steed of a Calormene lord and his training as a war charger. Furthermore, having spent less time in Narnia than most talking horses, he had certain incorrect notions of Narnian behavior and culture.
Bree had an inflated self-image due to his comparisons with non-talking horses alone, bolstered by his position as the prized steed of a Calormene lord and his training for battle. Furthermore, because he spent less time in Narnia than most talking horses, he held misconceptions about Narnian customs and behavior.