Biases in the operational sex ratio (OSR) are seen as the fundamental reason behind differential competition for mates in the two sexes, and as a strong determinant behind differences in choosiness. This view has been challenged by Kokko and Monaghan, who argue that sex-specific parental investment, mortalities, mate-encounter rates and quality variation determine the mating system in a way that is not reducible to the OSR. We develop a game-theoretic model of choosiness, signalling and parental care, to examine (i) whether the results of Kokko and Monaghan remain robust when its simplifying assumptions are relaxed, (ii) how parental care coevolves with mating strategies and the OSR and (iii) why mutual mate choice is observed relatively rarely even when both sexes vary in quality. We find qualitative agreement with the simpler approach: parental investment is the primary determinant of sex roles instead of the OSR, and factors promoting choosiness are high species-specific mate-encounter rate, high sex-specific mate-encounter rate, high cost of breeding (parental investment), low cost of mate searching and highly variable quality of the opposite sex. The coevolution of parental care and mating strategies hinders mutual mate choice if one parent can compensate for reduced care by the other, but promotes it if offspring survival depends greatly on biparental care. We argue that the relative rarity of mutual mate choice is not due to biases in the OSR. Instead, we describe processes by which sexual strategies tend to diverge. This divergence is prevented, and mutual mate choice maintained, if synergistic benefits of biparental care render parental investment both high and not too different in the two sexes.