As pointed out
here, my grammar in that sentence was atrocious. May I clarify:
Alanis Morrisette's song "Ironic" is quite catchy, but the situations described therein are not really ironic.
Which may be an irony in itself.
But it also makes the song 'wrong' in the same manner as a song about goldfish being titled "My Pet Trout" would be 'wrong'.
Trying to explain this to somebody who doesn't understand (or doesn't want to) is an exercise in frustration.
Quite possibly because (1) they like the song, and (2) they think they have learned something new.
Which is ironic, because they think they have learned about irony from a song entitled "Ironic" but they haven't, really.