In the play The Importance of Being Earnest the characters of Gwendolen and Cecily serve as mirrors of each other. Their characters are rather flat, since they do not change throughout the play. Yet, they are useful characters that present a social reality at the time the play was written: The silly nature of the courtship and marriage processes in Victorian society.
Gwendolen and Cecily are young girls who share an equal obsession to marry someone named "Ernest". They were fixated with the name and were willing to chose a man just for the sake of this detail.
When the two women met by accident at Jack's country estate they were already "engaged" to their respective "Ernests". Gwendolen was engaged to Jack, who used the fake name Ernest when he was in the city visiting her. On the other hand, Cecily's "Ernest" was none other than Algernon who came to Jack's country house pretending to be Ernest, the name of Jack's fake evil brother.
The shifting in the relationship of Cecily and Gwendolen began when they first met and acted as if they would be great friends. Yet, as their conversation progressed, Cecily and Gwendolen thought that they were both engaged to the same man. This caused a showdown between the two women during tea time, in which they declared war on each other, shifting from friendship to hatred.
Once the situation was clarified, the women shifted back to being friends. They were especially united when they realized that neither of their fiances was named Ernest. Because of this, the women became a united front and expected a dramatic apology from the part of the men who, unfortunately for the ladies, stayed behind eating the muffins and cakes that they women did not eat during their tea fight.
Therefore, the shifting relationship between Cecily and Gwendolen was based on their willingness to fight one another for the love of their "Ernest". However strong their bond might seem after they were clarified, one can tell that their so-called friendship is not based on a solid foundation and one can almost predict another showdown happening over something silly some time in the future.