Hermaphroditism is rare and phylogenically in decline among animal species. The evolutionary basis for this development is not well understood. This paper focusses on self-incompatible simultaneous hermaphroditism in animals. It proposes that such hermaphroditism is not stable in sufficiently heterogeneous populations, suggesting a possible reason for why hermaphroditism is rare among evolved animal species. The argument turns on the Bateman principle, namely that male reproductive success (RS) is limited by partner availability, while female RS is not. We show that: low-quality individuals do better if female; secondary sexual differentiation may be important for understanding the existence of males; and that hermaphroditic mating is reciprocal. Reciprocity may be key to understanding promiscuity and attendant phenomena such as cryptic female choice, sperm competition and love darts-common features of hermaphroditic mating. We also argue that hermaphrodites are especially vulnerable to male violence, suggesting a reason for the rarity of trioecy. Finally, we propose that external fertilization, and the scope for streaking, may be one reason fish are the only simultaneously hermaphroditic vertebrates.