Why did Cecily and Gwendolen quickly become angry at each other?

Mr Worthing (Jack) and Algernon or Algy, both are with Chasuble, the clergy, speaking about the christening, so Cecily is alone at home. But, suddently Gwendolen appears in the country. At first, both women think that they will be good friends because Cecily thinks that Gwendolen is uncle Jack's friend, who help him with the humanitan work of rescating his wicked brother Ernest. But they change mind, after a long discussion, both realize that they are engaged with the same man, called Ernest. As a consequence of this, Cecily and Gwendolen quickly become angry at each other, although, when both men appear, the girls are friends again. True?