The irony is biting.

It's ironic that a song about irony contains no actual examples of irony. But since that's ironic, is it actually an appropriately named song?

The song contains many instances of cosmic irony[0], as well as a few instances of other types of irony (e.g. "Well isn't this nice?").

[0] - https://en.wikipedia.org/wiki/Irony#Types_of_irony

Rain on your wedding day is not cosmic irony or any other kind. It's simply misfortune.

> presents agents as always ultimately thwarted by forces beyond human control

The implication of "rain on your wedding day" is that your wedding day is something you plan out extensively, trying to create some perfect event. And yet it can still be thwarted by weather. Obviously it takes some interpretation since it's a situation compressed into a 1-line song lyric but yes it can (and should, given that the song is called "ironic") be read as an example of cosmic irony.

What's more ironic, a wedding on a rainy day, or rain on a wedding day?