Goa'uld, aside from being endosymbionts, are aquatic predators that reproduce by spawning large amounts of offspring left to fend for themselves with only a few surviving to adulthood (traditionally labeled r-selected species). The symbiotes are androdioecious: the two sexes are males and hermaphrodites; in the absence of males the hermaphrodites may self-fertilize. Where their reproductive cycle becomes bizarre is that only an extremely small percentage of the symbiote population are hermaphrodites, which doesn't make sense in asocial species. In androdioecious species on Earth the hermaphroditic sex makes up the majority.
Why would the symbiotes evolve this way? It seems counterproductive to an asocial r-selected species strategy.
To clarify, while several characters state Goa'uld are "asexual" others state evidence to the contrary. This is probably just because the writers weren't biologists and didn't know the specific terminology. While queens (hermaphrodites) are capable of self-fertilization, non-queens (males) have been shown capable of inseminating a queen and passing on their genetic memories. The symbiote may hijack its host's reproductive system to do so (loosely similar to real life Sacculina) and as a consequence they may pass their genetic memories to the host's offspring.