Firstly, I was thinking what are Ionesco's characters trying to achieve? Obviously, the purpose of their existence is to reproduce. In fact, Father-Jacques claims it himself, "We must assure the continuity of our race."(pg. 131) While evaluating this purpose, I´ve realised that if this piece has antagonists it cannot be any of the characters but it is their dialogues.
The book is overfilled by incomprehension and useless exclamations.The only thing they are fighting against is the COMMUNICATION.
Actually, this is one the key points that Ionesco tried to highlight in his works. Communication is the crucial step how to achieve something in a group. And if it doesn´t work...just look at the nice example listed below. God punished us by confusing the languages at the tower of Babel because he knew that if we couldn´t communicate we would find it more difficult to unify on a huge tasks. He was/is the smart one!