This is a theory I've held for a long time, and so far I cannot see a reason why it doesn't work

The legendaries seem to be seen as one offs in the Pokemon world. Despite some repeated cries that they must be breeding, I see no theories (other than the asexual breeding one) that really explain this

So here. We. Go!

• The Legendary Birds

Some of the easiest ones to tackle, they are merely birds that, like the panda, are a bitch to breed in captivity. No way would the day care center have the resources (Articuno likely requires a cold mountain, for example). In fact, these legendaries aren't even stated to really be anything more than rare, powerful birds, further supporting that they are just picky about breeding

• Mewtwo

Why the hell would competent scientists create a killing machine able to breed? Nope, the only Mewtwo's are the ones they created. Unless, of course, they messed directly with Mewtwo's mother's genes. In which case... Uh, way to go scientists. Nice job screwing that one up

• Mew

Mew give live birth according to the journals. I suspect that maybe, being the equivalent of Poke Platypi (instead of being one of the few mammals to lay eggs, they are one of the few Pokemon to give live birth), they may just be picky

• The Legendary Beasts

These ones are a little tricky. There are clearly multiples... Right? I mean, there are three in Orre and one in Kanto at the same time? ...Except XD can also communicate with FrLg, yet that clearly occurs at a different time than Colosseum. So what's going on here?

Quite frankly, I have no guesses at all. Were they Eevee turned into Super Vaporeon, Super Jolteon, and Super Flareon? If so, then maybe Ho-Oh took inspiration from other beasts and raised these three into that form. Or maybe they are just closely related to Eevee and as such, once in a while, a trainer finds an Entei popping out of their Eevee egg and goes WTF. This one is one of the few I have to file under oddity, unless the ones raised by Ho-Oh were either a dead set of Legendary Beasts (kind of weak ass of Suicune to drown in rain, though) or were just the very first (in which case what the hell did they breed with and why are they picky now...?)

• Ho-Oh and Lugia

From what I can tell, they are based on some specific legends involving a female phoenix and a destructive male dragon - both forms of gods - being lovers. So I suspect Ho-Oh and Lugia are just the female and male (or male and female?) of their species and have some intense breeding rituals. Or Lugia can be of either gender and Ho-Oh can too. Either way, intense breeding that they don't like to do near humans

• Celebi

First one to have multiples of its species and not be a breeder. I suspect all Celebi are actually the same Celebi but in different points of time. Perhaps some events caused time line splits leading to multiple Celebi that aren't the same. Tl;dr - Celebi is a paradox waiting to happen

• The Regis

They are golems. Even Regigigas is said to have created a set. What's stopping humans from creating their own set of keys to seal Gigas away? So yeah, the first robotic Pokemon

• The Lati

...Do I really need to say it? There is a male. And a female. Preeeeetty sure they can breed

• The Weather Trio

They aren't exactly giant. Perhaps they are very solitary animals that only get out once every few years for a breeding frenzy, and otherwise rule over their own regions. Or maybe they only mate when there is a death (they influence weather. I choose to believe that they can tell when one dies)

• Jirachi

Once again, a breeder

• Deoxys

It's a virus. I suspect the way it proliferates is very painful for the victims who are soon to become Deoxys. In fact, I even wrote up something fairly long about this a while back. Basically, it infects a victim. The victim flees to its family, driven by the viral infection rewriting parts of their mind. Soon they change and then infect their family, who seek out others. So do your part and kill a Deoxys today

• Lake Trio

They were born from the same egg - at least the original ones were. These ones have some interesting powers, but yet even Frontier Brains can have them (...Somehow... I... Am not sure where they come across such powerful figures). But they can suppress even a god's power. What if one dies? I don't think Arceus would take that chance. I think he created more and gave them the ability to breed

• The Dragon Trio

...HgSs has an event where Arceus destroys and then recreates the universe to give Ethan an egg. And he needs his power boosted by Unown to do so. Suffice to say, any cases of their being multiples can be safely ignored as non canon (except for Ethan's baby Eldritch Abomination)

• Heatran

They can be a boy or a girl (Wait, Oak can tell the sex of that, yet not a human child?). Not much of a stretch here

• Cresselia and Darkrai

They merely balance each other out. Darkrai's ability is even described as a defense mechanism. Since Cresselia is female only, any chance that maybe Darkrai is the male of the species? Would be handy if you could go near your mate without them being subjected to endless nightmares, after all. I mean, heck, the only time we actually see the two FIGHTING are in Mystery Dungeon, which is hardly the same canon

• Manaphy and Phione

We know where Phione come from, and it's stated that Manaphy just require cold water (apparently the Day Care Center doesn't have cold enough water). That one is canon

• Shaymin

Just a rare hedgehog that only breeds in flower fields that the Daycare lacks

• Gigas

There are statues of them all over that get activated. And they are clearly long lived. Perhaps they are like the Dragon Trio in that what you see is what you get?

• Victini

Only really stated to be a rare Pokemon. So once again, very picky about breeding

• The Muskedeers

Nothing more in legend than fighting in a war. So nothing in legend argues against them being picky breeders. Maybe their mates died in the war?

• The Kami Trio

All male only. So I'd assume they only breed with their own species, and we just never see the mates

• The Tao Trio

Canonically there is only supposed to be once of each (hell, Reshiram and Zekrom can't even be shiny, so as to keep with canon). So uh... Only way more can exist is time line splits

• Meloetta

Once again only really stated to be rare

• Keldeo

Part of the Muskedeers, see the theory I have for them

• Genesect

An extinct species brought back to life and modified. I... I think Plasma neutered them, actually

• Arceus

He's God. I think he can damn well do as he pleases, even be owned by multiple trainers at the same time

Tl;dr - Maybe put on some Barry White...?