Jack is most angry about Algernon pretending to be his brother Ernest in order to propose to Cecily. He is furious because this deception not only endangered his secret identity but also endangered his relationship with Cecily. The relevance of this is that it highlights the importance of honesty and transparency in relationships. Jack believes that relationships should be built on trust and that deceit and deception can cause irreparable harm. Additionally, it showcases the theme of identity and the consequences of adopting false personas.
