What are the ironies we find in the tragedy Macbeth?
One of the most often discussed ironies is the character of Lady Macbeth versus the character of Macbeth. If one was looking for traditional male and female representations, representations that would have been usual in drama is Shakespeare's day, what we have here (in the early scenes of the play), ironically, is the exact opposite of traditional behaviour.
Lady Macbeth is decisive, apparently unemotional in her decision making, and without scruples. She does, in Act I, scene v, ask the dark forces to "unsex" her, but she honestly seems to be doing a good enough job on her own, "unsex"-ing herself. She taunts Macbeth for his more traditionally feminine concern over things like treating Duncan as a proper guest in their home, his fear over noises and things that go bump in the night, and his concern over behaving in the way that he "should. She calls his behaviour un-manly and all but tells to stop his whining and get on with the killing. This control that Lady Macbeth exerts would also have been much more of a traditionally man-as-head-of-the-household behaviour--a very ironic characterization.
And Shakespeare doesn't end his ironic portrayals of these characters with these early-in-the-play twists on their gender roles. In the second half of the play, he transforms them again, ironically, into the very close approximations of mirror images of how the other character behaved in the early scenes. Macbeth becomes a cold-blooded killing machine, one very similar to Lady Macbeth's early demeanor. And Lady Macbeth has been rendered sleepless and incapacitated by her guilt over the murder of Duncan, an echo of the early Macbeth.
Shakespeare plays upon the audience's traditional expectations of masculine and feminine behaviour in Macbeth to create a man and woman who, ironically, both surprise us with their out-of-gender behavior and then surprise us again with another ironic twist in which they seem to switch behavior, becoming much more traditional in their portrayals.