Chapter IV touches upon several aspects of Gatsby's and Daisy's characters that establish the irony in Gatsby's romantic pursuit of her. His quest for Daisy is ironic in that she is a woman he can never have. The scene with Meyer Wolfshiem in Chapter IV makes it clear that Gatsby is engaged in criminal activities; Wolfshiem is a gangster and Gatsby is, at the very least, a thief and a swindler. His role in society alone would exclude him from any relationship with the well born, socially respectable Daisy Fay Buchanan.
In the second section of the chapter, Jordan Baker tells Nick of Daisy's history with Gatsby when they first met in Louisville. Although Daisy had loved her young lieutenant, she could not or would not defy her family and follow him to New York to say goodbye before he went overseas to the war. She waits for Gatsby for a while, but then marries wealthy Tom Buchanan. Daisy cries for Gatsby on her wedding day, but she marries Tom as planned. In both these instances, Daisy is shown to be weak and indecisive; she lacks the will to challenge or defy the norms and standards of her social class. Even if she really loved Gatsby after meeting him again in West Egg and rekindling their affair--and that is questionable--she was far too weak and easily influenced by Tom's wealth and her own social station to commit to him. Daisy is beyond Gatsby's having; his devotion to her and his many efforts to achieve that dream are sadly ironic. With his death, they become tragically ironic.