You don't have to, the word Captivity has confined in the definition. That is why it is not a great word to use in this situation. For bad situations sure, there are places that do that. None of the AZA ones are. Those are accredited and must prove that the animals have above and beyond the resources needed, including space. It is disingenuous to still use that term and even those places have struggled getting away from using the word, but that is just a side fact.
This is the logical fallacy of circular reasoning. It is like saying "They do this because they do this." It is what they do with the animals in captivity that matter. There is countless evidence that has even been quoted here that AZA facilities must prove that they are educating and giving back to conservation of species. The endangered factor is kind of a misnomer in many cases because the Manatee was at most danger when it was taken off the endangered species list. Many zoologists hate when that happens for similar reasons as then they have to re-educate and explain how threatened and endangered works. People tend to not care as much when they hear that an animal is no longer endangered.
You also misquoted yourself and originally said they bred for purposes of entertainment. Now you are saying captivity. Two different situations there. Also entertained by animals does not mean make it inherently wrong. People like animals, they are fascinating. To counter that Many Zoos and Aquariums half more animals not seen by the paying public than on stage, so it is not really for entertainment at that point. This is a verifiable fact which makes your statements very generally dangerous.
Of course, one is welcome to feel a way, but without the full picture untruths are told.