The Fly is told from the perspective of The Boss, though it has a 3rd person narrator, making the point of view 3rd person limited. We see some development of The Boss's friend Woodifield, but just enough to understand The Boss's relationship to him and opinion of him. Woodifield is retired and seems to be dominated by his wife and daughters. While on some levels, the Boss seems grateful to not have just an influence on his own life, his thoughts and actions later in the story make us think that perhaps the Boss would have a more joyous life if he shared it with someone.
It is significant that the perspective of the story focuses on the Boss, but is not 1st person. The audience sees the contrast between the Boss and Woodifield more completely because of the 3rd person narrator. We are also able to see into the Boss's past with more objectivity (though not complete objectivity) because it is not being told to us by the Boss himself. This point of view also allows for suspense as the Boss repeatedly drops ink on the fly, and creates an environment to discuss and postulate why he behaves in such a way. Had the story been told by the Boss himself, those elements of suspense and thoughtful reflection would be removed, changing the way we understand Mansfield's thematic development.