The answer to this question depends on which part of the play you are referencing.
At the beginning of the text, Helena reveals that she is in love with a man named Demetrius who is romantically interested in Helena’s friend Hermia.
Hermia, however, is in love with another man named Lysander, although her father has arranged her marriage to Demetrius. While this does not necessarily constitute a quarrel, there is an underlying conflict between the two women, since one of them is left alone without a suitor.
Later on in the play, Hermia and Helena do engage in a verbal spat. This occurs after Puck mistakenly causes Lysander to become infatuated with Helena. Under this spell, Lysander denies that he ever loved Hermia. This causes Hermia to become angry with Helena, whom Hermia accuses of bewitching Lysander.
Unable to believe that anyone could be in love with her, Helena is perplexed by both Lysander’s and Demetrius’s professions of love—both of which were given under the influence of artificial love spells cast upon the men by the forest fairies. As a result, Helena thinks that both men are making fun of her, and she accuses Hermia of joining in their mockery.
Although this quarrel is resolved, the two women experience a test of their friendship in the forest outside Athens. Each of them insults or mistrusts the other because she lacks the full explanation of what occurs with the two male suitors. Ultimately, their friendship is restored once the truth is revealed and the marriages secured at the end of the play.