I once watched an episode of Martha Stewart where she showed us how to harvest carrots. She went to her garden and yanked up carrots the length of her arm. She bundled them up and placed them in her wicker basket. So when I was ready to pull out my carrots, I imagined the same results and being able to carry my wicker basket with honor and parade them around the neighborhood.
Ehh, not so much, DOC!
I suspect the soil was just too "hard". Next year, I'll make up a special area for carrots and mix in a lot of peat moss and other things to keep the soil soft enough for the carrots to expand.