Everyone handles grief differently. Some people succumb to despair, whereas others develop a more stoic attitude. The latter attitude even extends to the tragic deaths of loved ones, the very people we never thought we'd have to mourn in our lifetimes.
On the face of it, it would seem that Mr. Woodifield has a quite stoical attitude toward the death of his son in World War I. He's able to talk about the recent visit of his daughters to his son's grave without any real emotion, an indication perhaps that he's able to keep his feelings in check, an important element of the ancient philosophy of Stoicism.
At the same time, one could argue that what appears to be Stoicism is simply an expression of Mr. Woodifield's growing senility. It's not that he's chosen to mourn his son's death in a particular way, but rather that the way in which he mourns has been imposed upon him by the aging process.
In any case, Mr. Woodifield's way of handling grief is different from that of the Boss. When Mr. Woodifield mentions the recent visit of his daughters to the war graves in Belgium, all the Boss's feelings of grief are immediately triggered. Though he manages to keep his feelings in check for the duration of Mr. Woodifield's visit, the Boss has been plunged into despair and is on the verge of tears after the old man leaves.
Now that his grief has been stirred, the Boss needs to find a way of banishing the profound unhappiness that he feels. In this story, he does this by torturing a fly to death. Only by doing this can he forget why he was so sad in the first place.