Fish and ants do not show any signs of suffering in terms of emotional pain and introspective agony—especially if one of their own gets snagged by a predator. Nor do the hawks flying around in the cold rain for prey complain about the hostile conditions. The rabbit may scream when the hawk snatches it, but is is suffering or is it a survival mechanism to cause the hawk to drop it?
Only humans suffer the way the Buddha describes it. He learned about suffering when he left the artificial heaven of his father’s palace and saw that every household had someone in it who had died. He saw illness. He saw decrepit old age. These are things his father was trying to shield him from. But he saw clearly that no one escapes from this suffering.
So he set about to find a way to relieve this uniquely human condition. The human mind despairs, contemplates its mistakes, plots revenge, holds anger, feels interminable grief—unless. Unless we find the way out. He tells us that the source of all this suffering is our attachment and desire for something else than what we are now going through or what we now have. He tells us give up this desire for something else and face what is.
Then he gives us the Noble Eightfold Path as a recipe for a clean, wholesome, spiritually connected life in the here and now. He is honest about the existence of suffering, unlike some religions that claim that our pain is only an illusion. And he is very practical about how to go about alleviating it for ourselves and others. But to say that “all life is suffering,” is incorrect and I doubt that he really said it that way.