[drtom]

Once lifeforms become more complex (i.e. with specialized cells) a pure cell splitting process won't work anymore and reproductive systems that carry the entire genetic code evolve.

Some plants can get by on self-pollination but, again, with rising complexity, you need two partners in order to avoid cumulative deterioration ("the incest syndrome").

Next step up are hermaphroditic lifeforms (mostly invertebrates) which do not have separate sexes. In these groups, hermaphroditism is a normal condition, enabling a form of sexual reproduction in which both partners can act as the "female" or "male".

Some hermaphroditic individual animals favour to act as a particular gender (although the other set of reproductive organs seems to be fully intact) which could be argued as the forerunner for split sexes.

Through evolutionary processes one set of organs gradually ceases to function while the other is being enhanced. Do this over a few hundred million years and you have a new taxonomic group of lifeforms that presents with two distinct sexes.

In a nutshell, you are correct: the two sets of organs did not evolve separately and turn out to be complementary "by accident".

[gitmo]

And throw in alternation of generations, where plants generations alternate between beng haploid and diploid. That further complifies the simplicated.