"The Child is the Father of the Man."
The positive and life nurturing impressions that get deeply etched in our minds when we are small children remain with us for the rest of our adult life. These early spiritual life sustaining childhood memories form the foundation of our adulthood and determine our personality. Hence, a happy childhood filled with pleasant life giving positive spiritual influences -here symbolized by the pleasant associations linked to the beautiful rainbow - is the 'father' or the creator or the architect of a mature adult, the 'man.'
The Child is the Father of the Man., The Child is father of the Man. Which one is correct?
"The Child is the Father of the Man." is a very interesting sentence since it is polysemic. However I will try to develop only one of its aspects here. We can suggest that The Child is a silent figure, the act of speaking being a kind of liberation i.e. a kind of lie. (because we cannot reach objectivity properly speaking)
The Child (as a symbol) does not lie. This symbol can be construed as the quintessence of man, as his uplifted soul, as the climax of consciousness. Then we might say that "The Child" is a purified image of man. It is widely known that (more often than not) a good child becomes a good man, a good husband and a good father. Out of hand we can notice that there is an everlasting chain of three figures: (Child --> Husband --> Father) which are intrinsically connected to each other.
My answer is rather uncomplete however I hope it will be useful.