Anyway, it's a pretty simple concept - the trainers will sell/train you a companion but only the pet of your toon's race. It costs 50 silver, and regardless of the trainer you speak with, they will only offer you your race's home pet.
So for the raven, you'd need to be a Worgen to purchase that particular pet since that companion is the Worgen's "home pet". If you're a Night Elf, the trainer will offer you a Great Horned Owl instead, if you're a Troll you'll only have the option to learn the Black Kingsnake, and so on.
The newest race, the Pandaren, get the Jade Crane Chick. I suppose this is an incentive to create a Pandaren if only just for the crane pet.
It should be noted that if you don't especially WANT to play or keep a toon of a certain race, but would still like their home pet, you could create an alt, learn both Battle Pet Training and the companion from the trainer (to purchase the pet requires the ability to pet battle), and then delete that character. Doing this won't remove the pet from your journal.
For those that have already filled up all character slots on a server with certain races and can't afford to delete or add any new ones, you could create another toon on a different server of any race you don't already have. Once you have their race's home pet, you could then delete that alt. I'm 90% sure "account wide" means cross server too, so you'll have access to your shiny new companion despite having learned it on another server. Yay! :D
Alternatively, you could simply head out to a vendor that sells the pet. Most of the companions that are associated with each race already have specific vendors and actual pet items that you can purchase. I'm not sure if these vendors are going away in MoP, but I doubt it.
The only new companions that you can't buy off of a normal vendor are the Gilnean Raven (Worgen), Shore Crab (Goblin), and Jade Crane Chick (Pandaren). It should be noted that the chick does have an actual item ID for it, but it's not clear if it will be up for sale from a vendor or not.
Last but not least, remember that in MoP the vendor filter will have a mind of its own, so you might need to check and uncheck some of the filters to get the Battle Pet Trainer to show you which companion is your race's home pet.
And as always, this is still the beta so things could change and how it currently functions might not be how it works in the final release.
UPDATE: Here's a list of each race and their purchasable/trainable companion from the Battle Pet Trainer. These are subject to change.
Draenei - Blue MothHorde
Dwarf - Snowshoe Rabbit
Gnome - Snowshoe Rabbit
Human - Orange Tabby Cat
Night Elf - Great Horned Owl
Worgen - Gilnean Raven
Blood Elf - Golden Dragonhawk HatchlingPandaren - Jade Crane Chick
Goblin - Shore Crawler
Orc - Black Kingsnake
Tauren - Brown Prairie Dog
Troll - Black Kingsnake
Undead - Undercity Cockroach