You know, I've reconsidered my criticism of Alanis about that. It's true that, as written, nothing in the song is ironic. However, many of them are conducive to irony with additional facts. She's writing a song, not a dissertation so maybe we should cut her some slack.
For instance, rain on your wedding day is of course not ironic. But some people, fearing rain on their wedding day, intentionally hold weddings in places where precipitation is rare. And if you scheduled your wedding in the desert to avoid rain, and on that day, it rains in the desert for the only time that year and it doesn't rain at home -- that's certainly ironic.
If a ride used to be free, and then the operator decided to charge money, and upon learning that there would be a pre-pay discount, you pre-paid, and then the operator scrapped the charge money plan without a refund, that would be ironic.
Ten thousand spoons when all you need is a knife -- all right, I give up on that. Irredeemable. Maybe the irony is that Alanis thinks people can relate to that and it's why she chose it, only to find out that almost nobody has experienced the problem of excessive spoonery.