Maybe it's like Tracey ends up with 4 chocolate bars and ¢25

This kicks ass, you rule

That's an Ikea faucet, right? I had to do the same thing a couple of days ago. I ended up dremeling (drilling, effectively) two holes in what was left of the aerator, as far apart from each other as I could, and twisted the thing out with some round nose pliers pointing upwards. The top of the aerator is much more solid than the brittle honeycomb below it. I am now waiting for an adapter piece from China that will allow me to screw on a different type of aerator, externally, so to speak, so this can't happen again.