Ballet class (Dramatic Irony)
At boxing one day, Billy sees a ballet class practicing in the other part of the gymnasium and goes and joins in. While it awakens a deep-seated passion within him, he does not tell his family, fearing that they will disapprove of his new interest. He takes the money that his father gives him for boxing lessons and uses it to pay for dance lessons instead, which creates a situation of dramatic irony; while we know that Billy is becoming a promising young dancer, his family members have no idea.
Billy preparing for his audition (Dramatic Irony)
After Tony and Jackie find out that Billy is dancing, they angrily disapprove and insist that he stop. However, Billy's passion is stronger than their disapproval and he soon goes back to Sandra for help in preparing for his audition to ballet school. Their secret rehearsals continue the trend of dramatic irony, with raised stakes. Now, not only do we know that Billy is dancing without his family's knowledge, but we know that he is dancing in spite of their objection, with plans to audition for ballet school.
Jackie's approval (Situational Irony)
For much of the film, Jackie seems like a brutish (if deeply-feeling) man, someone who would never want his son to be a ballet dancer. In fact, when it is revealed that Billy is taking ballet lessons, Jackie is furious and forbids his son from continuing. Thus, it is especially ironic when, after seeing his son dance in the gymnasium one night while his gay friend Michael watches nearby in a tutu, Jackie completely changes his tune and begins to support his son's love of dance. This change of heart is unexpected and changes the course of the plot completely.
Billy's Acceptance (Situational Irony)
Billy's audition for ballet school goes incredibly wrong when he punches a kid in the face and answers the interview questions defensively and inarticulately. Even his dancing is awkward and he seems nervous and ashamed as he goes through his routine. Thus, it is somewhat ironic when he gains acceptance to the school. The filmmaker, Stephen Daldry, plays up this irony by making it seem as though Billy will likely not get in. As Billy reads his acceptance letter, he barely makes an expression, seeming miffed more than excited. Thus, it is a huge twist when his family comes in the room and he tells them, straightforwardly, "I got in."