The poem is called "On My First Son," so naturally family plays an important role here. The poem reflects on what it is like to lose a child, but also about how one's ideas of fatherhood are altered after the death of a child. Can a dad still be a dad after such a tragedy? That's the kind of question that might not have a final answer, a lot like "What's the sound of one hand clapping?"
By not directly calling the child his "son" (except for in the title), the speaker makes it seem as though the child is somebody else's. In this way, he lessens the tragedy of the situation by distancing it from himself.
The speaker's idea of family is strangely limited and one-dimensional, a lot like our drawing skills. Without his son, he wants to abandon all thoughts of fatherhood, as if he wants to abandon any role as the head of a family.