I am learning English by reading the poem "my heart leaps up". I hope that in the near future, I will come to love poetry enough instead say: "I am learning English that I might read poems". I have been trying to memorize the poem and when I read it, I wonder why he wrote:"the child is father of the man" but not "the father". Is it correct to speak like this in real life?
Yes, we speak that way in real life. You can say "father", "a father", or "the father". They are equally correct but have different meanings. Without any article, "father" becomes a concept rather than a specific person. The poet could have said "the father" but he chose not to do that for two reasons: (1) he is more interested in the idea of "father" rather than a specific person, and (2) the rhythm of the poem is better without the article.
The poem has iambic form. That means that the syllables alternate soft, hard, soft, hard, etc. Using capital letters for the strong syllables, the line looks like this
the CHILD is FATHer OF the MAN
So, you see, if he had said "the father" this rhythm would have been totally messed up.