The irony of tradition as a negative force
Typically, heritage and tradition are positive, and we often carry positive aspects of world cultures as good things, but for Chinese tradition, there are aspects that don't line up with Spring Moon's sense of justice. Tradition can thus be seen as a bad thing, which is the grand irony of the novel.
The irony of pluralism in China
When China changed in the 20th century, it was the death of a tradition that spanned for thousands of years. It was truly an ancient civilization, and even though the changes of industrialism were across the earth, China's change is particularly tragic, since that tradition seemed impossible to defeat. As history has shown, the idea that a tradition can be protected from change is simply unrealistic.
The irony of Lustrous Jade's hopeful engagement in society
Spring Moon didn't necessarily intend to pave a future like the one Lustrous Jade chooses for herself toward the end of the novel, but that's the irony of progressivism—by leaving behind certain aspects of tradition, a person paves the way for their children to abandon the tradition entirely. That's not what Spring Moon wanted, necessarily.
The irony of feet binding
One of the central ironies is something Spring Moon has to deal with herself, the ironic practice of damaging young girls' feet to make them prettier somehow. This unfortunate aspect of Chinese heritage is a great example of how the force of tradition to preserve things doesn't always mean that the practices preserved are necessarily helpful or good. Spring Moon is smart enough to figure this riddle out though, and she chooses not to damage her daughter in the same way her mother damaged her.
The irony of ancestors
By appealing to the views and desires of ancestors, it seems like there is an appeal to some objective standard, but ancestors are dead. Their influence is only what each person takes them to mean, which is ironic, since the entire premise of ancestral honor is to help shape someone's worldview. Turns out, it's a social construct, much like other aspects of Chinese heritage. It is as meaningful as a person makes it.