The Irony of the Film's Title
Batman Begins is not the first Batman film (nor the first Batman origin film) ever produced. However, it is the first Batman film to tell his story in this way. Not only does it show a portion of his well-known origin story (i.e. his parents being murdered), it shows how he obtained his world-class crime-fighting skills.
The Irony of Loyalty
Bruce was once an integral member of Ra's' society, yet later fights against them. At first, Ra's and Bruce were very good friends and fought together hand-in-hand in Ra's secret society. However, once Bruce learns of Ra's' sinister plans, he ignores their friendship and his old membership in the secret society and fights to stop him.
The Irony of Speech
Rachel tells Bruce that good people do nothing, yet the audience knows that Bruce is the Batman and fights crime. With that said, she does not know that Bruce is Batman and thus cannot know that he is fighting for good.
Who Owns WayneCorp?
Early on, one of the high-level executives at WayneCorp tells Bruce that the company is owned by a number of groups and charities. Towards the end of the film, Bruce repeats the same lines to that same executive to tell him that he now ultimately owns the company -- not those charities and groups.
Irony of Compassion and Loyalty
Towards the start of the film, Bruce saves Ra's, yet towards the end of the film Ra's doesn't reciprocate when Bruce needs to be saved. In fact, he does the opposite: he tries to ensure Bruce dies. The audience doesn't expect Ra's to help Bruce; they also don't expect him to help ensure that Bruce dies.
