Jack is prevented from revealing Algernon’s assumed identity to Cecily because Algernon has already charmed her, and she believes they are engaged.
When Jack returns to his country house, he is furious to find Algernon there pretending to be his (fictional) brother, Ernest. Jack wants to expose Algernon’s deception, but before he can, Cecily excitedly announces that she and "Ernest" (Algernon) are engaged.
This surprises even Algernon, but he plays along. Since Cecily is already deeply invested in the idea of "Ernest" as her ideal romantic partner, Jack realizes that revealing the truth immediately could upset her and cause more chaos.
This forces Jack into a difficult position, allowing the misunderstanding to escalate further, leading to the play’s hilarious climax.