Before 4.0.1 there was one pet to rule them all, Wolves that brought Furious Howl. If you didn’t bring this one pet then you were doing it wrong. It was the same back in Burning Crusade, but back then the same situation applied to the Cat rather than the Wolf.
Cataclysm came and Blizzard redesigned pets to apply raid buffs:
5% increased stats
Shale Spider (exotic only) - Embrace of the Shale Spider
Burst haste
Core Hound (exotic only) - Ancient Hysteria
Stamina
Silithid (exotic only) - Qiraji Fortitude
10% attack speed
Hyena - Cackling Howl
Serpent - Serpent’s Swiftness
5% spell haste
Sporebat - Spore Cloud
10% spell power
Water Strider - Still Water
5% critical strike
Hydra - Bellowing Roar
Wolf - Furious Howl
Devilsaur (exotic) - Terrifying Roar
Quilen (exotic) - Fearless Roar
Water Strider (exotic) - Still Water
Increased mastery
Cat - Roar of Courage
Spirit Beast (exotic) - Spirit Beast Blessing
Weakened armor
Raptor - Tear Armor
Tallstrider - Dust Cloud
Physical vulnerability
Boar - Gore
Ravager - Ravage
Rhino (exotic) - Stampede
Worm (exotic) - Acid Spit
Magic vulnerability
Dragonhawk - Fire Breath
Wind Serpent - Lightning Breath
Cast speed slow
Fox - Tailspin
Goat - Trample
Core Hound (exotic) - Lava Breath
Physical damage reduction
Bear - Demoralizing Roar
Carrion Bird - Demoralizing Screech
If you have mostly physical DPSers, for example, the physical vulnerability debuff is going to help you more, whereas if you have more magical DPS the magic vulnerability will help you more. Most of of all was Ancient Hysteria could for its haste buff.
This forced Hunters to bring only the pets with these buffs or required them to go tame one of these pets to have when needed. You would show up to a group and there would be someone looking at all the hunters to tell them what pet they were to switch to, or run back to a stable to get that pet.
The Blues didn’t not like that Hunters should be forced into taming particular pets, so they removed raid wide buffs from pets in Legion.