Quick Answer: It is a misconception that bears can't talk in BoJack Horseman. It is only Herb Kazzaz's nurse who can't speak English. According to show creator Raphael Bob-Waksberg, while most animals in the world of BoJack grew up speaking English, there are still some bears that only speak "bear."
While anthropomorphized characters might run amok on the Netflix series BoJack Horseman (2014 - ), it seems that certain animals are more humanistic than others. This had led fans to wonder a simple question: If horses and dogs can talk, why can't bears? Though it may not be the most thought-provoking question that the show has elicited, it is a valid one considering all the animal inhabitants in the BoJack universe do speak English. However, when it comes to bears, they only seem to grunt unintelligibly. Or do they?
The first bear we meet in BoJack Horseman is in the second episode of Season One, "BoJack Hates the Troops." In one scene, we see a bear angrily protesting in front of BoJack's home. We hear him go on a tirade in fluent English for several seconds, but since the scene is so short, most viewers tend to forget about this bear.
A protesting bear in front of BoJack's house
The next bear we meet is in episode six of Season One, "Our Story is a 'D' Story." In the episode's intro, we see Mr. Peanutbutter (Paul F. Tompkins) waiting in front of the airport holding up a sign for Diane (Alison Brie) that says, "Honey." A bear then walks up to the sign and mumbles, "Huh?" before sighing and walking away. Though the bear doesn't say anything intelligibly, Mr. Peanutbutter seems to understand her and she seems to understand him. Presumably, the bear is also literate, recognizing the sign's promise of honey. This scene is the first instance of a bear not speaking in English.
A bear "talking" with Mr. Peanutbutter
The next non-English speaking bear we meet is Tina, the nurse who aids BoJack's former mentor Herb Kazzaz (Stanley Tucci). Tina's odd manner of speaking is what left many viewers confused. She appears to be the only animal character that speaks in her "native" language. Whenever we see Tina interact with other characters, we only hear her growl and groan, but nobody seems to notice or mind.
Tina giving a funeral eulogy while speaking in "bear"
In a Reddit AMA, show creator Raphael Bob-Waksberg revealed that the bear from the airport is in fact Tina, although this isn't made entirely clear in the television show. Bob-Waksberg said, "There ARE bears that talk, like the guard at the prison, but Herb's nurse doesn't. Don't quote me on this, because I might change my mind later, but I like to think that English is still a language that needs to be learned in this world, and while most animals grow up speaking it, some bears still only speak bear."
While Bob-Waksberg's answer isn't necessarily canon, there is one instance of an animal learning how to speak English in BoJack. In the fifth episode of Season Two, "Chickens," we meet a runaway chicken named Becca who befriends Todd (Aaron Paul). It isn't exactly clear why Becca can't speak, but the episode suggests that it is because she is a "food chicken" that was treated with hormones. It is also possible that Becca cannot speak English because she was isolated from the rest of the world when she was living on a chicken farm.
Although Todd and Diane are worried that Becca's lack of language skills will make it difficult for her to survive, Becca shows signs of retaining names and language. By the end of the episode, we hear Becca attempt to pronounce Todd's name. Since Becca spent the majority of the day with Todd, Diane, and Irving (Amy Schumer), we can assume that human contact can stimulate language skills in animals.
Because of Becca the chicken and the few other English-speaking bears in the show, we can assume that Tina can also learn how to pronounce names and speak English. If we ever see Tina again, it's probably just a matter of time before we hear her speak, or perhaps she is simply more comfortable speaking in "bear."