I guess that, as
@Composer99 suggested, this may just be a matter of differing definitions. To me, an ability that allows taming of animals and monsters is basically an invitation to find combat-effective creatures and make them de facto animal companions, making it a de facto pet class.
Okay, but I didn't say they'd be able to tame anything beyond what a given DM would allow with any PC with Animal Handling. They'd probably have advantage on a lot of checks due to being to communicate more easily with beasts and then later other creatures, but if the DM doesn't allow that sort of thing anyway, this Ranger doesn't circumvent that.
I guess the fact that they could choose not to do so may make it technically not a pet class, but it certainly seems like it could be used as such.
I guess I'm also just not willing to nix design concepts because they
could be used in a way that some people don't want to be forced to do if they play the thing. That's what we have here. You said you don't want to have to play a pet class in order to play a ranger. I'm saying, okay, you wouldn't have to.
I may have missed your earlier comments about not allowing taming of wild animals. The first post I saw from you that described the concept was the following:
I can see where the idea of taming came into it for you, but every single time I've replied to you about it I've reiterated that gaining a pet wouldn't be a necessary component of the concept.
To me, "befriending" creatures that the ranger can "turn to their side" sounds pretty much like taming, at least on a basic level. If you've stated elsewhere that this is not the case, I apologise for missing it.
And even if you could gain a pet, it would take time, it couldn't be brought back without burning the same magic you'd have to for a PC, and it would be dependent on either multiple skill checks or the use of spells (animal friendship, for instance). And that's
if it was decided to even allow such a thing at all.
What is more likely, is a sidebar saying that if gaining a pet via Animal Handling is allowed in the campaign in general, the Ranger is better at it than others are.
Now, even if we ignored the desire of some to not play a pet class in any way, and said that the ranger could make critters fight for them, assuming we could even balance that without an unacceptable level of abstraction (which, once you reach a level where full casters can turn enemies against their allies, the balance is probably fine), it takes a long time to turn a creature into an actual pet, unless you're a Beastmaster. Even if you use spells, they only last for so long.
So,
at most, we'd be looking at a class that can get low-int enemies to chill out and leave the party alone, and by then spending some time with a single critter, could befriend it and cause it to be friendly toward the ranger until the ranger gives it a reason not to be. If that creature is amenable to fighting, this could mean some limited combat help, while the ranger is in the creature's territory, roughly equivelent to animal friendship and various charm spells. At no point would the class give you a pet, outside of the BM subclass and/or an optional find familiar variant, and in a campaign where pets are generally allowed, the Ranger would just have some benefits to the checks involved to accomplish that, they wouldn't be guaranteed success.
But getting a balgura to lead you to a safe place and stand watch while you rest would be awesome enough to be worth the class feature at higher levels.