The answer to this question can be found at the beginning of Chapter Six, when Lenina discusses Bernard with Henry in bed. Henry is rather brutal about Bernard, comparing him to a "rhinoceros." This is what he says about him to justify this comparison:
"You can't teach a rhinoceros tricks," he had explained in his brief and vigorous style. "Some men are almost rhinoceroses; they don't respond properly to conditioning. Poor devils! Bernard's one of them."
Bernard therefore is a rhinoceros because he does not respond to conditioning, which is of course the major force of this fascinating future dystopia which is presented to us in this world. Not responding well to conditioning means you do not fit in to a world which is built around being conditioned so that you are happy and satisfied with your lot in life, rather than feeling discontented and desiring more, as Bernard does.