The story of Martin and his relationship, his love with Sylvia has to do with the idea of, what would happen if a socially accepted taboo were performed. And to make the stakes even higher, Albee has Martin commit the offense while he has just won the Pritzker Architecture Prize and has been chosen to design a multi-billion dollar city. These details are put in for the audience to know that Albee is asking a big question, what happens to a city and its design when the architect's belief system goes out of bounds of what is natural?
This question plays out as well on in Martin's relationship with his wife, Stevie who cannot fathom how her husband has done this. She is unwavering in her belief that they are a couple who know deeper things than most married couples. That they have endured and were seeking to endure together. To her this is what great love it. Thus, when Martin claims that Sylvia the goat loves him as much as Stevie does it sends her into a ferocious state. One where she sets out to prove if this is true, which results her slitting the goats neck and dragging it home to show how far she is willing to go to love Martin. That nothing will stand in the way of what she believes to be the design for their lives.
Albee includes Ross, a friend from a television network as a secondary character in the play in order to reveal the role of the media. Specifically, the fact of how the media decides what is acceptable or not. It is only what is shiny and can be presented to the public with bells and whistles that is acceptable. Why? Because it makes them money. It also opens up the idea that the media is the judge of the truth, a dangerous practice that has become the norm in America. Dangerous because the truth and humanity is filtered out.
Finally, Billy is Martin and Stevie's son. He is a teenage boy, who ends up confessing his love for his father and kisses him on the lips. Albee is connecting that what the parents do has a great deal of influence on the child and what they will deem to be healthy. Thus, because Martin has crossed a line that is taboo he gives his son permission to do the same without directly saying it. Albee is showing the effect of an ostensibly liberal society from the perspective of the family.
