Why do they call it teething if there are no teeth?

What a week. After all the rescheduling of babysitters, I thought I could relax a little...
But, then the teething began. The salon feeding was the last good feeding for hours...and hours...and hours. Kira suddenly seemed to find it painful to eat. She would act so hungry, but would pull away and stop after just seconds. She wouldn't sleep, either. That night, it took 2 of us over 3 hours to get her to finally fall asleep...in my bed next to me no less. She would wake up every hour or so, sit straight up in bed and scream. Wah! I was so sad for her. We got out the tylenol, teething tablets, and teether toys from the fridge. Nothing helped dramatically, but at least she would calm down after grabbing a cold toy and furiously rubbing it on her top gums.
So, why then are there no teeth to show for it?
We had 48 hours of very little nursing and little to no eating. 48 hours of broken night sleeping and only 30 minutes of napping during the day. And lots and lots of chewing, drooling, and rubbing the gums. Lots and lots of heartbreaking cries. But, NO TEETH! I don't get it. Shouldn't teething lead to at least a little glimpse of a tooth? Maybe just a shiny spot on the gums? Nope. Nothing.
Finally, after a good sleep last night and a lot of nursing and napping today, Kira is more her happy self. But, we are still waiting for the teeth...and dreading the teething.