He was a boy, she was a girl
Can I make it anymore obvious?
I failed to pick up on this one on first hearing, because I was living in heteronormative land and in fact believed myself to be straight. But let's give Avril the benefit of the doubt and assume that she's being ironic and aware and all of those things. It is, after all, a pretty well-known trope that if you have a boy and a girl, there's going to be some kind of romantic subplot.
He was a punk, she did ballet
What more can I say?
But "punk/ballet" imply something as heavily as "boy/girl" implies a romantic subplot. What could that be? The charitable interpretation is that they're self-evidently a mismatch - that you should stick to dating your own kind - which is somewhat at odds with the "see the soul that is inside" implied moral. Don't judge based on appearances ... but if he's a punk and she does ballet it's never going to work out.
But wait. Let's look at a couple of other lines.
She had a pretty face but her head was up in space
Does your pretty face see what he's worth?
The implication here is that "she" is conventionally attractive but lacks other admirable qualities. Maybe "what more can I say" is meant to suggest that's what you'd expect from someone who does ballet - which is a pretty heavily female-coded activity. Later in the song, the narrator - who I'm calling Avril for convenience - positions herself very firmly as superior to this girl who does ballet and is so shallow as to judge a boy based on the clothes he wears, as well as a better fit for his male-coded preferences.
He wanted her, she'd never tell
Secretly she wanted him as well
Here's where it gets creepy. At this point, Avril could be an omniscient narrator with access to the thoughts of every character. But at the end of the song, she reveals that this is a song she and the Sk8ter Boi wrote together about the girl. So if she'd never tell, and Avril only has access to the boy's thoughts, how exactly can she know that the girl secretly wanted him? Maybe he just wasn't her type. For all we know different, she wasn't even into boys at all. We have the word of a boy who fancied her and whom she turned down that she totally wanted him, and how much is that worth, exactly?
Five years from now, she sits at home
Feeding the baby, she's all alone
I used to just skim past this line, assuming she was "all alone" in the sense that her partner was out at work and she was sitting around bored during her maternity leave. But in fact, this whole verse is showing what a dismal life the girl has now, so I'm guessing it's actually meant to mean she's a single mother. Because as we all know, single motherhood is one of the worst humiliations that can be inflicted on a woman.
She calls up her friends, they already know
And they've all got tickets to see his show
Her friends sound pretty crap, really. If someone I went to school with hit the big time on MTV, I'm sure one of my friends would at least send me a facebook message about them. But her friends apparently don't know that she used to know this boy, and furthermore they've all got tickets to a show without asking her if she wants to come along. Wow, she's really not having any luck in life, is she? And wait, remind me again how Avril and the boy know what's happening in her life?
She tags along and stands in the crowd
Looks up at the man that she turned down
Nope. The very first phrase of the song said that he was a boy when she turned him down. Five years down the line, he isn't the same person. For all we know, back in those days he was a dickhead of the first order and needed all those years of growing up before he was fit to be seen in public. Although, since he co-wrote this song with Avril and hasn't reined in any of her spite, he might still be a dickhead of the first order.
Sorry girl, but you missed out
Well, tough luck that boy's mine now
We are more than just good friends
This is how the story ends
She's basically gloating that the boy is now dating her and not the girl. With, and I cannot state this too many times, no evidence at all that the girl even wants to date him. I wonder whether she's protesting a little too much? He remembers his old crush vividly enough to co-write this song about her, after all, and maybe Avril's picking up on that.
About ten years ago, I wrote a comic that was supposed to be from the boy's point of view. The girl turned him down because she was a lesbian, and actually had a full and happy life when he spotted her in the audience at one of his shows. He waxed nostalgic in Avril's hearing about how different they both were back in those days, and Avril turned it into a song about how the girl was such a terrible shallow person despite his protests that it wasn't like that at all. And eventually the whole thing spiralled out of control and broke them up. That is how strong a hold this flaming song had on me.