The thing is that it's one of the suggestions that comes up when you put "Why won't" into Google.
Which means that someone really rather odd has trained Google into thinking that that is a common question that people are likely to want to know the answer to.
But don't fear for the future of the human race just yet. There's a reason someone has done so. It's a game, a jeu d'esprit. The full explanation of "why won't my parakeet eat my diarrhea" is here.
This actually all looks like a variation on "googlewhacking". That's the attempt to get your page as the only entry in the entire Google index for some phrase or another. You do have to be pretty inventive to manage it now, given the size of the index. My assumption is that this is a variation: a game being played to see who can get the most outrageous suggestions out of Google by asking the question a few times and seeing if it comes up as one of those suggestions. And I would think that whoever came up with "Why won't my parakeet eat my diarrhea?" has managed to win a very large number of points.
What fun, eh? Anyone coined a word for the game yet?