the challenge with satire is that it often relies on a bit more life experience than a 13-yr old often has. This is not a criticism, just an observation. In the same way older folks may not get your inside jokes among your peers, some stuff is only truly funny once you've had kids of your own.
At their heart, most Onion articles are about taking one aspect of something we recognize (in this case, a huffy tween, which you have to admit is a sort of person that does exist) and exaggerating it to show how ridiculous it is.
The deeper humour is how it shows the irrational feelings we have about other touchy subjects, like euthanasia of people that the state feels may no longer be capable of thought or feeling, and how families are affected by such decisions.