Where are all the female orcs?
I have to admit that one of my favorite bits of speculation/inference in Middle-earth studies is the problem of the orcs, their origin and reproduction. Here's are the inter-related suites of problems as succinctly as I can express them:
To have exciting battles, you need lots of cannon fodder (which is why in FRPGs the generic term for relatively weak bad guys who are easily killed is "orcs").
Morgoth and Sauron, by theological definition, "cannot make, they can only mock," that is, they cannot generate ex nihilo free-willed (or pseudo-free-willed) creatures to serve them.
So you need a source for orcs.
The only free-willed creatures in Middle-earth are Valar and Maiar ("powers," angelic/demonic spirits), the "Children of Iluvatar" (elves and men), and a kind of special dispensation given to the dwarves, ents, and apparently the eagles.
So, I think Tolkien reasoned, the orcs were somehow transformed elves, elves who had been subject to torture until they became orcs.
But this clashes, possibly, with his reincarnation of the elves idea.
And there's an associated problem, that the production of countless orcs for cannon fodder purposes then requires a very extensive operation of elf-torture over many years, even years when Morgoth and/or Sauron are not present in Middle-earth.
So, you could let the orcs breed (and at least in LotR and Silm there are hints that Tolkien adopts this idea).
But breeding is problematic, as it includes elements of sexual pleasure (we'd assume) and even more so that someone would have to love and nurse the cuddly little baby orcs. And so when you're spearing Shagrat, you're killing some mother's beloved son.
I think towards the end of his life, JRRT was tending towards making the orcs having been men who volunteered for Morgoth's evil and were thus transformed (doesn't solve the breeding / raising innocent little cuddlesome orc babies).
But I think there might be a simpler explanation, consistent with both the origins of the word "orc" and the later development of Tolkien's thought regarding the reincarnation of the elves.
"Orc" comes from Beowulf 112; a list of monsters includes "eotenas ond ylfe ond orc-neas", usually translated as ettins (trolls), elves and animated corpses (in some of his earlier work Tolkien translated orc-neas as "barrow wights"). So we have the concept of the animated corpse.
Now, what animates the corpse? Here I turn to the philosophical essays in Morgoth's Rings. Morgoth, in his attempt to control Arda, became like a glacier of evil, calving off bits of evil throughout the world. He puts forth some of his spirit, and gets Glaurung, and when Turin kills Glaurung, that little bit of evil is gone from Morgoth. Thus Morgoth grows smaller and less powerful the longer he is in Angband, but the amount of evil in the world stays the same or grows slightly larger as his evils creations work evil into the very fabric of the world.
Now, where does the corpse come from? I think from elves. Tolkien's original ideas about elves and orcs could work if the process of elvish reincarnation that Tolkien eventually settled on were to work. There are, for elves, two components in a living creature: a Fea, or spirit, and a hroa, or body. And, Tolkien says, the Fea creates the body (he got this idea from Charles Kinglsey's The Water Babies but don't you dare steal it because I'm writing it into an article for Chris Vacarro, whom I went to high school with, but I digress...).
So, if an elf's body, his Hroa, is killed, his spirit, Fea, goes to Mandos to wait until such time as it is appropriate for him to grow a new body (Tolkien ended up rejecting the idea that the elf spirit would be borne as a baby to its parents, or to some other parents, etc).
So, if Morgoth captures an elf, and tortures it until its spirit leaves its body and goes off to Mandos to grow a new body, the old body remains in the possession of Morgoth. He can imbue that tortured body with his dark spirit, thus making a orc without creating something new.
I know there are some subtle problems still, but for the sake of argument, let's say that the above can explain the origin of orcs: Morgoth has calved off bits of himself and set them in elf bodies. It explains the "animated corpses" connection and the "not allowed to make" objection.
But once Morgoth was cast out of the Doors of Night, where did the new orcs come from? We're back to breeding in some way. I'd propose some kind of hideous rite in which the orcs hack off pieces of their limbs, which then re-grow into new creatures. These each have the same identity of the orc from whom they are chopped, so they're immediately viciously rivalrous with that orc. That way you squeeze out sexual love and familial affection. Maybe orcs force other orcs to breed because the process is so miserably painful.
So really this is just a long train of bizarre speculation set off by Emma Goldman's interesting post on the possibility of female orcs in Middle-earth.