Although Bernard Marx is an Alpha, his short height makes him feel as if he does not belong amongst the high caste. As a result, he is incredibly rude to his inferiors, as well as to other members of his own caste.
This is a controversial argument in today's society: does height really matter? Studies suggest that it does: in the end, height affects perceptions of leadership ability. Taller men are perceived as more commanding than shorter men. Studies have regularly shown that random people will pick the tallest person from a group as being the most commanding, even though in reality he might be inferior in rank. The honour guards in most militaries around the world regularly induct only the tallest men.
Because of the perceptions that have been built up by our society, shorter men can feel inadequate and insecure, even if they have superior abilities. Despite what every feel-good guide and common sense may tell us, height unfortunately does matter in our society.