Father and Son
Martin is having sex with a goat, yet ironically when his son confesses he is homosexual and kisses him he flies off the hinges. It is okay for him to commit bestiality, but completely wrong in his judgement to be gay.
Explanation
Martin does his best to explain to his wife, Stevie how his relationship with Sylvia the goat is possible. He tells her that she is a soul and loves him as much as Stevie does. Ironically, this explanation leads to Stevie slitting the throat of the goat, ending Martin's relationship with it.
Trust
Martin confides in Ross, one of his oldest friends about his relationship with the goat. Ironically, Ross doesn't seek to help his friend. He simply tells Stevie through a letter and shuts down any appearance Martin will have on his television station.
Architect
Martin's profession is an an architect. He is an award-winning architect. Ironically, though he is a man of design Albee has him go out of human design and have sex with a goat.
Cheating
Stevie finds a woman's business card in Martin's clothes. She thinks he's cheating on him, but ironically the woman's card is for a bestiality support group that Martin is seeking help in.