We might chew our food because we have tiny mouths and throats, but there are actually tons of animal species out there that prefer to swallow their food whole and have jaws capable of expanding wide enough to make this possible.
A recent study revealed the capabilities of the dragonfish, which appear to have a hinge joint in their heads that has never really been seen in a fish species before. This allows the dragonfish to effectively open their jaws as much as 120º. This number is, of course, dwarfed by snakes, which can sometimes open their jaws by as much as 180º.
Once the jaws are open, it's a matter of using their sharp, inward-pointing teeth to trap the prey so they can't escape, then slowly walking them into the stomach with special muscles dedicated to the process. In snakes, the creature just continues to move forward until the mouth completely engulfs its prey - the dragonfish on the other hand probably uses forward swimming momentum to do the same.
So why do some animals swallow their food whole rather than chewing it to bits like we do? Some experts believe that it's probably because of energy consumption. Some creatures have more of a need to conserve energy than others, especially dragonfish, which live at extreme oceanic depths and don't see much prey.
These kinds of creatures have stronger stomach acids that can break down even harder substances, like bones and eggshells.
So, is swallowing food an evolutionary advantage that lets creatures conserve more of their energy while eating? Some might agree so, but it's still not much more than a theory at this point in time.