It raining on your wedding day isn't ironic unless you're marrying an umbrella shop owner who has recently gone out of business.
Being stuck without a spoon to stir your tea in a spoon factory would be ironic.
It's like good advice you just can't take? No?
>It raining on your wedding day isn't ironic unless you're marrying an umbrella shop owner who has recently gone out of business.
Rain on one's wedding day isn't by itself ironic (in England for example it would be par for the course, as it almost always rains anyway).
But it can be, under certain expectations (e.g. an expectation and preparations for a ceremony with nice weather, sudden rain ESPECIALLY on that day, when it was all well and sunny for weeks before, etc).
Actually most (if not all) of the examples in the song are actually ironic. And the example given above is not the sole definition of irony (but could be an ironic situation).
From the dictionary:
(a) the expression of one's meaning by using language that normally signifies the opposite, typically for humorous or emphatic effect.
(b) a state of affairs or an event that seems deliberately contrary to what one expects and is often wryly amusing as a result.
The "10000 spoons when you all you need is a knife" is obvious with the latter example.
As for the "rain on your wedding day", it fairly obviously presupposes the expectation (of the "stereotypical" woman planning her wedding) that it would be some perfect sunny day.
E.g. imagine a bride to be planning her reception, and after weeks full of summer sun, it pours like crazy in her wedding day ("a state of affairs (...) deliberately contrary to what one expects and is often wryly amusing as a result") -- it's this feeling like the universe is mocking you, like you know, the weather changed on purpose.
Of course a song has to tell those things elliptically, and people expect to see irony either in the form of (a -- most comments I've seen allude to that) or in a blatantly explicit (b).