It's instructive that the title of the play alludes to the derivation of the word "tragedy," which comes from the ancient Greek for "goat song." In ancient Greek drama characters were often punished by the gods for transgressing cultural norms. And that's what's happened in the case of Zifa. He has been cursed with impotence for failing to adhere to the appropriate burial rites. By burying his father too early after he succumbed to leprosy, Zifa has ritually polluted the land, thus invoking the wrath of the gods.

The overriding theme of the play, as in many of the Greek tragedies by which it is influenced, is the futility of defying fate. Zifa, no less than Oedipus, is ultimately destroyed by failing to realize this.

The primary and most obvious theme in Song of a Goat is the problem of the main character, Zifa. He is an influential man who is married to Ebiere but is infertile, or sterile and impotency. Ebiere wants a child and consults the village masseur, who is also the village sage, or wise person. The advice Ebiere is given is that Zifa should give permission for her to bear a child fathered by Zifa's brother, an acceptable cultural alternative to childlessness. This is unacceptable to Zifa and to Ebiere. This theme is literal and symbolic at the same time as it also stands for the other theme of a person rejecting themselves as inadequate. Zifa feels he must reject himself if he owns up to infertility by accepting the alternative offered by the masseur. In the end his brother Tonya and he do reject themselves in the ultimate act of rejection. There are also themes about conflicts between between the ideas held by the young and those held by the old as well as about folklore's symbolism.