Hi. I just clicked on 'Hatch Me!' for a creatu that was fully incubated and was met with the message: Sorry! Your attempt at hatching this egg has failed. Did I do something wrong? I had just gotten the egg today and it was fresh. Thanks for any help I can get on this.

You did nothing wrong. If you look on that chart in the Hatchery, you'll notice that even Fresh Eggs have only an 85% chance of succeeding. This is in order to keep pets from becoming too overpopulated and to keep the prices for them more stable.