I think you are led onto a false path partly by the typical problems with natural language that is woefully inadequate for rigorous reasoning.
"Can pigs fly" is a sentence with only three words, but all of them are ill-defined.
Additionally, you do not specify time and location, both of which are crucial.
"Can" may mean "able to survive survive" (as in "can humans breathe helium") or "able to perform an act actively" (as in "can I lift a 100 pound weight"). This difference is crucial when we talk about whether pigs "can" fly: The active act is very impossible, but there is a finite chance that they survive flying through the air, depending on the altitude and the manner of landing. How we interpret "can" is connected to our interpretation of the next word, "fly".
Another common problem with "can" questions is that they may ask either about what we could call an "innate capability" — or about a non-zero possibility of a future event. The two are distinct questions, even though they are connected: Because the term "possible" implies that the world is not pre-determined but includes random events of different probabilities, every "possible" event has a finite chance to happen during some finite time interval in the future (and a probability of 1 if we say "ever"!) And if somebody answers "yes" to the question "can you do X?" they may well be asked to prove it, by performing the act.
One problem with the idea that "can" asks about a non-zero probability of something actually happening in the future is that the future may be very different from the present, so that different things become possible.
"Fly" generally only means that something is airborne. Among the possible ways to be airborne is flying by actuating wings, like a bird, or staying suspended on a ballistic trajectory, like a missile, or being suspended by the wind, like a kite. There is probably also a measure of time involved because "jumping" is not "flying": We are in the air, but only briefly, and then we fall down. Competitions involving "flying" are very careful to define parameters like altitude and duration.
Flying like a cannonball or being lifted by wind is clearly conceivable with pigs. All kinds of objects have been lifted into the air — one of the interpretations of "fly" — by strong winds, among them cows and Dorothy in her house.
Are we talking about the Domestic Pig, sus domestica? Or she suborder suina, a much larger group of mammals of various sizes, including possible extinct species? I think none of them could fly actively, but I'm less sure about that than about the sus domestica with which I am reasonably familiar.
The main reason I'm asking is that a wider definition may include future species which may very well develop the ability to fly. Reptiles spawned a flying branch; why not pigs. If we ask whether there is a chance that any pig ever can fly, the answer is certainly yes. We cannot exclude such a development.
As mentioned, predictions are difficult, especially if... you know.
The question probably takes it for granted that the pig is on level ground on Earth around sea level, because in different places like the ISS pigs could easily fly.
If we understand the question "naively", imagining a sus domestica attempting to perform powered flight (excluding jumps) on Earth on a calm day at sea level on a level surface, it is physically impossible. But this is not the only way to understand this sentence. In order to get proper answers you need a clear definition of what you are asking. Part of being specific is whether you are asking about a future possibility (which is implied when we talk about probabilities) and whether you include the past. The past is only imperfectly known; the future is essentially unknown.