"Miss Searle had always considered boredom an intellectual defeat"

Miss Searle's quote suggests that she thinks that dullness signifies a lack of intellectual engagement. She likely believes that if one is bored, it is due to the fact that they are not tough themselves intellectually. She might also think that boredom signifies complacency and an absence of curiosity. She likely believes that a person ought to strive to be intellectually engaged and curious in order to avoid monotony. She might also think that boredom is a sign of a lack of imagination and creativity. Miss Searle's quote implies that she values intellectual engagement and curiosity, which she believes that dullness signifies a lack of these qualities.