He does this because he's saving the universe.
The Incubators are much like classically biblical angels or modrons; they aren't creatures of heaven or any other supernal realm, but they are Gnostic stewards of the material world, utterly dispassionate and removed from the anthropomorphic perspective. They take on this form only because it is useful, and they are in truth a single group-mind that expands all possible bodies simultaneously.
Kyubey is only visible to those it chooses to be, and approaches adolescents in times of emotional stress and desperation in hopes of forming Contracts. He supports them passively, and as they collect and use Grief Seeds, he eats them, all the while waiting for the moment to bring down the hammer and push his clients into becoming Youma, if they don't collapse on their own. A killed Puella Magi is a wasted investment, and too many dead humans means his cattle don't breed as many suitable clients, but that's the only reason he pretends to care at all.
As for the Grief Seeds he takes, he does not destroy them. Grief Seeds are sent to wherever Incubators come from, where their endless suffering is milked for free energy; that's what this is all about. The energy the Incubators collect from their schemes is used to stave off the heat death of the physical universe. Perhaps they're the only reason it's lived as long as it has.
Again, the Incubators are not malicious. They can't be. They withhold information but they do not lie. They do not do physical harm, only say hurtful things. They have no emotions, no empathy, no grudges. All that matters is acquiring more energy through the Contract system, and they gain energy from the initial Contract, the transformation into the Youma, and eventually the collected Grief Seed.
Mechanically, treat them as any sort of small ferret-like animal; they have no HD and no AC. Any attack against them automatically hits and is an instant kill. It doesn't matter, however, as a new Incubator body just teleports in and eats the corpse to preserve the calories. And they don't care. They'll keep saying whatever they want to say via their telepathy.
Besides telepathy, forming contracts, and having infinite teleporting vessels, Incubators can't really do much. Treat them as having INT 30, or whatever the equivalent is for godlike intelligence. Literally, only a god or multiversal hivemind can outpace them. Assume that an Incubator knows everything through atomic omniscience; they can listen in on the telepathy they give Puella Magi but they cannot read minds. They cannot see the future, or anything magically protected against them, but they essentially have cameras everywhere in the world.
They will never attack you, though they tend to say things designed to hurt you. Always polite and sweet; after all, they have no ill will towards humanity. They just don't understand why you're crying over one little girl, sacrificed to save the universe. Thousands of more little girls are born every second. What does it matter?
They are the personification of Utilitarianism, taken to its most inhuman, strawman conclusion.
Youma, that which Puella Magi are born to fight. The source of curses, which are themselves born of curses. Youma are inhuman, fae, eldritch creatures that don't follow normal logic, and cannot live in the material world. Instead, they create pocket dimensions known as Labyrinths to protect themselves, and stalk mankind in the shadows.
A labyrinth essentially is a bounded space in the Ethereal Plane, overlapping the real world along a different axis. Any Puella Magi (as well as anyone of sufficient magical accumen), can open a Gate to a labyrinth in the area by pure will; labyrinths are as dungeons, with the top level being closes to the real world, and each level beyond taking you further from real-world imagery into the Youma's inner sanctum. For instance, a candy youma might haunt a hospital, and indeed there's syringes, exit signs, false nurses, and the like in the top layer, but as you go deeper, everything is eventually replaced with gingerbread houses and ice cream mountains.
The reason it's so easy to enter a labyrinth is essentially that Youma are able to invite people in and out, as with a Mage's Magnificent Mansion, though due to their goals and warped minds, they by default are 'inviting' everyone. A Youma can shut up their lair and keep anyone from invading it, but then they wouldn't be able to hunt or interfere with reality, either.
When a Youma is born, it is a personification of the Puella Magi's last, darkest emotions; it is, in fact, literally the poor child, having lost all hope in their soul and entered a permanent, irreversible madness. Their Soul Gem becomes the Grief Seed, and their body is discarded as they become an entity made of pure elemental Grief. Their form is a result of this symbolism. Here's some examples.
Mechanically, treat a Youma as statistically being the monster they look like; if they look like a dragon they do dragon things, otherwise get creative. Their Hit Dice should be equal to their former Puella Magi level, though this isn't an inviolable rule. If our Dragon-Youma is extra scary with extra HD and she had the karmic potential to justify that sort of thing, go for it. If the Youma's truly less fearsome than it appears due to being an illusionist-Magi, or otherwise based on her insecurities and low self-image, roll with it. These are sentient, malicious symbolism engines and should be treated as such.
In addition, they have the spellcasting of their former Puella Magi selves, save that they don't benefit from their Charisma in regards to anything like bonus spells or what have you, and their Corruption Pool doesn't benefit from the Charisma bonus.
A Youma's Corruption Pool works differently; it starts full, and it drains to refresh spell slots. Corruption can be used to heal itself like a Puella Magi, but it doesn't gain any other benefits. A Youma returns to a Grief Seed if its Corruption Pool is drained to zero, which it also does if brought to 0 HP.
Youma can leave a Cursed Kiss at-will. This leaves an Arcane Mark that functions as a Charm Person, except that the victim is compelled into suicidal self-destruction. Murder-suicides, homicides, school shootings, suicide cults, people belly-flopping from high buildings, these are all caused by a Cursed Kiss. Sometimes its as tragically simple as someone in a hospital bed closing their eyes and just not waking up, due to lack of will to live. Puella Magi are immune to this ability
When someone under the Cursed Kiss dies, the Youma feeds off the despair, gaining 1d8 Corruption Points per HD of the victim. As mentioned, these Corruption Points can be used to heal, recover spell slots or create a Shikigami for 5 times the Tsukaima's HD in Corruption Points.
When a Youma dies and becomes a Grief Seed, their Labyrinth is destroyed; their Shikigami escape into their own lairs, living creatures reappear in the real world, and any unattended objects, including corpses, are seemingly lost forever.
Shikigami are like a witch's familiars. They are like lesser Youma in many respects: They can't live outside of labyrinths, they are made of solid Grief, they feed by Kissing mortals and killing them.A Shikigami is a soulless creation of a Youma that exists to serve them; like set-pieces in a dreamscape, they exist to fulfill a specific role and duty, and that is the totality of their existence. They never have more than half the HD of their master. 1 HD Youma cannot produce Shikigami.
A Shikigami cannot cast spells, though they can donate their Corruption Points to their mistress or heal themselves. A Shikigami can be released by their creator to form their own, smaller barrier and hunt on their own, though this will automatically happen if a Shikigami outlives its Youma. A Shikigami has Corruption Pools equal to their creator's, which start off empty. If it's filled up completely, the Shikigami matures into a perfect clone of its mother Youma in every respect, capable of dropping a Grief Seed even; it's supped upon enough mortal souls that it cobbled together its own out of the detritus fragments of pain.
What about in worlds where Youma don't exist? We have Akuyo. They're essentially Youma, but are not born from human suffering, but a mysterious universal rule. As if they exist to fill the void, and for no other reason. They drop 1d3 Curse Cubes per HD, which cannot hatch into Akuyo. Nor do they have Labyrinths or Shikigami; they merely haunt the Ethereal Plane, as if they were ghosts. Their Curse Cubes are generated by draining emotions from humans; the attacks of an Akuyo inflict Energy Drain. Someone fully drained of this attack do not die, however, but become emotionless level-0 NPCs. Puella Magi, however, are totally destroyed spiritually, vanishing into thin air so that not even the benevolent Law of Cycles (the universal rule that prevents Witches from being born) can save them.
An Akuyo gains a permanent new HD every time it drains levels equal to its own HD+5, unless those levels come from a Puella Magi.
Akuyo are not made of grief and curses; they are Lawful, extraplanar beings born of the will of the universe. A universe that fears the power of human emotions, strong enough to change its nature. As if to balance that karma, they act like perverse Bodhisattvas, out to directly murder passion.