Wordsworth's poem speaks to the power of childhood in the formation of one's identity. The poem articulates a condition of universal subjectivity. The vision of " a rainbow in the sky" is the natural element that unifies the speaker's, presumably Wordsworth's, sense of identity. The beauty of the rainbow, "so was it when my life began; So is it now I am a man; So be it when I shall grow old," is timeless. It serves as a way to connect the fragmentation to one's consciousness that is the result of age.
It is here in which Wordsworth suggests that there is much to be learned from childhood. "The child is the father of the man" is his way of articulating how childhood provides the basis for the growth and maturation of the individual. Wordsworth suggests that a significant way for an individual to understand their own condition in the world is to examine their own childhood. The experiences that Wordsworth has as a child has played formative roles in developing his identity as an older man. For Wordsworth, the man grows from the child within the individual. In the child being "the father of the man," Wordsworth suggests that the innocence of childhood and the moments that help forge who we are as children play formative and vital roles in the life we lead when we become older.
Another interpretation of this phrase is that of the son [the child] becoming a father to the man [the father] as roles sometimes becomes reversed with aged parents.