So why are there two genders, male and female, instead of only one or, say, three genders?
There are no stupid questions.
Lots of “lower” organisms are asexual (which is the same thing as unisexual). Some lizard species have actually lossed the male members of the species and are all female. So, there are many organisms that have only one gender and many that have two.
Three genders? Maybe that did evlove at some point but was weeded out.
Two genders is a result of sexual reproduction. Without sexual reproduction an organism’s offspring can only carry the same genetic material as the parent. This means that in an a environment that kills the parent all the children, grandchildren etc will also die. That isn’t a great survival strategy. So sexual reproduction evolved. With sexual reproduction it is possible for an organism’s offspring to have genetic material that the parent doesn’t have. If the environment kills one parent the offspring might still survive. That’s a much bete survival strategy.
Once you have sexual reproduction you need some way of getting the gametes, or sex cells, together. In the earliest sexually reproductive organisms this was done by releasing them into the water to let them swim around until they found each other. This works reasonably well, but once the cells have fused to form a new individual they need to start feeding really fast or they will die. This can be overcome by loading the cells up with food that they can use while they grow, but they then literally become fat, to fat to swim fast. A better strategy was to produce two types of sex cells. One of them could then be a fast swimmer, and the other could be big and fat with plenty of food to feed the new organism and just sit around waiting to be found. The immobile fat cell was the first female cell (ovum) and the small fast swimming cell was the first male cell (sperm).
Originally all organisms produced both male and female cells. They were effectively male and female together. Most organisms on the planet are still like that, they’re hermaphrodites.
Having different sexes for different animals probably evolved many times, but for two primary reasons.
The first reason is cheating. If an organisms was born that only produced male sex cells it has an advantage because they are much cheaper to make than those fat female cells. Rather than wasting energy producing ova it can shed lots more sperm into the water and they will find all the ova, or at least lots more than their competitors. That’s a great trick, but because it is successful very soon their won’t be many animals left that produce eggs. Most of the sperm will just die without finding a mate, and while sperm are cheaper to produce than ova they aren’t free and can’t be wasted indefinitely. At that stage it becomes advantageous to be female. All the purely male animals are wasting all their energy putting out sperm that mostly die, while all the ova that the females produce are garaunteed to be fertilised. Very soon the females will start to increase in number and after a while a balance will be struck and the genders will be fixed.
The second reason why different sexes evolved is specialisation, and more importantly movement specialisation. Being hermaphroditic didn’t work very well once organisms developed fast swimming abilities. While organisms are producing both ova and sperm they must compromise between what is best for the ova and what is best for the sperm. They can’t become too small because they need resources to produce and carry the large ova. They can’t be too large or they won’t be able to move towards potential mates fast enough to beat competitors. Essentially the ability to swim fast had imposed the same problem on the whole organism that had been faced by the first sex cells. And the same solution was found. Some organisms cheated and became male. They could swim around very fast and impregnate
Two strands of DNA, two copies of each chromosome, two sexes – very neat. What would the third sex do, babysit? 
Oh yeah, the three genders thing?
Well as you can see there is no real point in having three sexual types that are al needed at the one time. It doesn’t significantly increase your odds of having kids with good genes but it does make it much harder for the gametes to find each other. It also makes it much, much harder for offspring to inherit a recessive survival trait, which in itself probably explains why it wouldn’t work.
However there are many species that have three ‘genders’. These are normally male, female and psuedofemale. Males tend to be aggressive and fight over females or territory. The females are physically distinct form the males. Psuedofemales are reproductively male but physically look/smell/act like females. They exploit a third gender niche by sneaking in under the guard of the true males, who ignores them or even tries to court them. While he isn’t looking they mate with the real female. A clever strategy and one that is seen amongst molluscs, crustaceans and fish and I’m sure many others.
Other species have three genetic genders, but not at the same time. One generation will have male and female that produce gametes. When the gametes fuse they produce a third ‘sex’ that reproduces in its own way, either sexually or asexually and in turn gives birth to male and female offspring.
Fungi have mating compatability types controlled by multiple genes, so there can be thousands of different ‘sexes.’
But almost certainly face about. Separation of genetic material into paired chromosomes almost certainly occurred to facilitate sexual reproduction. It wasn’t the cause of it. There is no particularly compelling reason why an organism couldn’t have evolved three pairs of chromosomes if that was how sexual reproduction occurred. The two DNA strands is true enough, but a fairly minor problem.
After the cat jumping thing I’m almost scared to ask but…is the two DNA strands thing a “fairly minor problem”? How would three combine?
Two parents to not provide one strand of DNA each, but rather a half-set of chromosomes each. A chromosome is a long, coiled-up double-helix of DNA. Standard sexual reproduction does not involve a “male” single-strand bonding with a “female” single-strand. It involves a set of double-helixes from the father sitting in the general vicinity (i.e. a cell) of a set of double-helixes from the mother.
A three-sexed species could have three sets of chromosomes (which is called triploid, a state that occurs in nature, though not in animals that I know of), or the three sets could mix it up and discard a third of their total genetic material. The latter seems a drastic solution and I’m not aware of a precedent, though I’m not an expert.
In response to the OP, “genders” are not biological roles, but rather social roles. Non-reproductive members of a population (such as homosexual or infertile people) could be considered as seperate genders. If there is a genetic component to attributes that discourage or prohibit reproduction, they could even be selected for. It’s beyond me to come up with what niches they occupy in the reproductive process, but I’m sure somebody out there has a theory already.
What I don’t understand is how the leap from asexual to heterosexual was accomplished. At one time, all cells in amoebas and whatnot, were asexual. So how did, or how could, this have split into two separate genders.
Or, am I erroneous in thinking that all cell-level life is asexual?
The leap is not such a great one. There’s a convenient “missing link” (so it’s not really missing): it’s possible to reproduce sexually despite lacking sexual distinction. The sperm/ova thing only becomes an issue when you’re multicellular.
Some bacteria mingle their genetic material without reproducing. And I don’t even know where to start about Paramecium.
There’s a certain amount of evidence that the real driver for gender development was parasitism.
Levin, D. Am. Nat. 109, 437-451 (1975).
Jaenike, J. Evol. Theory 3, 191-194 (1978).
Hamilton, W. D. Oikos 35, 282-290 (1980).
Bell, G. The Masterpiece of Nature (University of California Press, Berkeley, 1982).
I wasn’t implying any causative relationship between double-stranded DNA, twinned chromosomes, and bisexuality. I just think it’s neat.
Ah, now we’re cooking with gas.
So, let me repeat this back to you, to make sure that I understand it.
As single celled beings became multi celled beings, and split off into specific species, it was at that moment that genders and sexual reproduction became solidified.
Am I understanding this?
A minor hijack here to ask a related question…
I know that at the genetic level the difference between the sexes in humans is the X-X vs X-Y chromosome pair. I also know that the Y chromosome is “stunted” or “incomplete”. (I’m sure someone who knows genetics knows the proper term here but I’m also sure you know what I’m talking about.)
Anyway, is the stunted Y chromosome unique to humans or is this a common characteristic of all males? Is there any theory as to why this one chromosome would be different from the other 40 odd pair?
Not really:
Speciation happens in non-cellular organisms now and presumably back in pre-cambrian times, and they may have sex as well ( eg chlamydomonas sp.). Sexual reproduction appears to be one response to unfavorable conditions and may be abandoned permanently or temporarily by some species in favourable conditions (aphids, some lizards fish etc.).
You could answer the OP just by looking at the numbers.
With two genders 2 conditions have to be met for reproduction to occur:
Male must be acceptable to female. (i.e. biologically, socially, status, health, fertility, etc… etc…)
Female must be acceptable to male.
With three genders 6 conditions have to be met.
Gender A must be acceptable to Gender B.
Gender A must be acceptable to Gender C.
Gender B must be acceptable to Gender A.
Gender B must be acceptable to Gender C.
Gender C must be acceptable to Gender A.
Gender C must be acceptable to Gender B.
This makes the whole affair 3 times as complex for no real net benefit. 3 times as many points at which reproduction could fail. It’s a distinct evolutionary drawback.
cos twos company, threes crowd 
The original question is a fascinating one (anything but stupid) and has not been answered in a way that satisfies everyone. First let me comment that whatever selective advantage sex has, it has some very real costs and three sexes would have much higher costs and probably no real advantage, so it seems unlikely.
The fact that it benefits a species in case of environmental change is no argument. In order that a mutation spread, it has to benefit the carrier (or at least his close relatives) here and now and not at some time in the indefinite future. That is why the parasitism theory is so popular. There are other theories however; I don’t know any easy reference but a persistent googler ought to be able to find something.
Finally, a comment on the XY method of sexual determination. It is universal or nearly so in mammals. My daughter once told me that bird have what is called WZ method. Here there are two chromosomes named W and Z and males are WW, while females are WZ,
I wonder where those names come from. The X and Y were already in use when I was in HS in the early 50s being taught that there were 24 chromosome pairs (there are actually 23) and the fact that X is the 24th letter of the alphabet makes me think that it comes from that. Nowadays chromosomes are numbered (in order of size, I believe).
Oh yes, one other point. Scientific American had an article about this maybe a year or so ago and it turns out the X chromosome has been decreasing steadily in size and has disappeared in at least one mammalian species (so females are XX and males just X) and it predicted that the same thing would happen with humans. The reason is that no important protein can be coded there (except sex dterminers) because all mutations would be dominant. So anything important migrates to another chromosome. There remains the question of sex determination, but that is not insoluble since at least one organism has solved it.
If boybeast & girlbeast require an itbeast to serve as a catalyst for sexual reproduction: itbeast “hooks up” with boybeast on one occasion & stores some genetic material, and later has a similar tryst with a girlbeast and mixes the genetic material within its beastfactory and produces either boybeast, girlbeast or itbeast as offspring (and there is no other way to create bb, gb or ib); can itbeast be considered a third gender?
And let’s go nuts: If Itbeast takes genetic material from two independant species (amazon river dolphin) and (komodo dragon) to create ONLY itbeast, what sexual designation would itbeast have if this were the only way to get an itbeast? What would the ‘donors’ be called?