Two studies investigated: (1) how people react to research describing a sex difference, depending on whether that difference favours males or females; and (2) how accurately people can predict how the average man and woman will react. In Study 1, Western participants (N = 492) viewed a fictional popular-science article describing either a male-favouring or a female-favouring sex difference (i.e., men/women draw better; women/men lie more). Both sexes reacted less positively to the male-favouring differences, judging the findings to be less important, less credible, and more offensive, harmful, and upsetting. Participants predicted that the average man and woman would react more positively to sex differences favouring their own sex. This was true of the average woman, although the level of own-sex favouritism was lower than participants predicted. It was not true, however, of the average man, who – like the average woman – reacted more positively to the female-favouring differences. Study 2 replicated these findings in a Southeast Asian sample (N = 336). Our results are consistent with the idea that both sexes are more protective of women than men, but that both exaggerate the level of same-sex favouritism within each sex – a misconception that could potentially harm relations between the sexes.