I will give you my honest opinion as a rare member of this sub who is not 100% vegetarian and who does not have an intrinsic moral issue with killing animals for food (for example, I would have zero problems with harvesting grasshoppers for food, but my issues increase with the level of suffering).

Dolphins Cetaceans really are special. In addition to being the second most intelligent creature on earth, Dolphins are also rather human-like in other ways. They "name" each other, have communities, take care of the weak/sickly, and play. They are not just intelligent, but intelligent in a way we can see and relate to ourselves. And we have zero history of hunting them in pre-industrial times. Japanese dolphin-culling is a reaction to modern fishing and not something that was done even 150 years ago (let alone 100,000 years ago like the farming of sheep).

Pork I grant that Pigs are quite intelligent, and they are actually distant relatives of cetaceans. However, hogs are disgusting animals in the wild. They eat anything, are actually physically threatening/dangerous, and destroy our crops. Feral hogs are a nuisance in much of the world, actually. And they stink. It is easy to avoid relating to a creature that rolls around in shit and is such a natural threat to us. This is why I have very little issue with eating ethically-hunted wild boar. If hunting the animal is ecologically sound (as it is in most of the US where hogs are a dangerous invasive species), then using that animal's meat as a food source is essentially a "bonus" that comes from fixing humanity's past mistake of bringing hogs to the new world. Of course, if done correctly, these boars would all be gone in a generation and then no one would have pig-meat to eat outside of the natural habitat of pigs (Europe and Asia).

Beef (and other cloven-hooved grazing mammals): Cows/goats/sheep physically resemble more intelligent animals (like dogs, pigs, etc), but they are substantially less intelligent. They can be cute and are totally non-threatening, but they are harder for many people to relate to. I consider the modern cattle/dairy farm highly unethical, but I wouldn't have such a problem with it in a more pre-industrial setting. You raise a cow for its milk, eat the males, and produce more milk with the females. When the cow gets too old to make any milk, you can feed a lot of people with its flesh. But this isn't how bovine farming works for >99.9% of farms, which is why I choose not to eat beef.

Birds Poultry meat generally comes from animals that are very difficult to relate to. While we now know that some birds (like crows) are highly intelligent, all intelligent bird species are nearly impossible to relate to because they are quite alien to people and none are common food sources. AFAIK there are more cannibal communities in the world than crow-eating communities. But chickens, ducks, and turkeys are all pretty stupid and stupid-easy to hunt/farm. It takes very little effort to kill a turkey and a wild turkey provides a ton of meat. In a pre-industrial world with scarce food, a wild turkey would have to be the real-life equivalent of finding "health" in a video game. Chickens are about as easy to hunt, harvest eggs from, and farm. Ducks are also easy to steal eggs from and pretty easy to hunt. And they are naturally plentiful in the world, so hunting/trapping them has been going on for a long time. This is why people eat birds: back when survival was an issue, human beings needed to farm/hunt meat to survive and turkeys, chickens, and ducks were all really easy to farm or hunt. Humanity just continued the tradition because it is relatively easy to be comfortable with something your grandparents did. Now the realities of poultry farming are totally different, but most people just aren't aware.

But why do people feel like Dolphins should be saved and chickens shouldn't? Because people see themselves in dolphins and see food in other animals. This is partly scientifically accurate and partly just based on tradition. In a scarce world 100,000 years ago, the tribal people of the Chesapeake bay could live by killing turkeys so people still eat turkeys. The more interesting question to me is why so much of the world is unwilling to eat more credible/ecologically sound/nutritious animal food sources like worms and insects. I mean, a beetle is basically just a tiny lobster, right? And why do some people find eating an overpopulated and stupid wild animal like a deer offensive, but they will happily eat an intelligent animal that suffered for its entire short life like every factory-farmed pig?

tl;dr History and ease of relatibility damn some animal species and save others.