If you ate it right away, I am not surprised it was too tough. It gets softer as the dressing permeates it, so is better the next day. I use everything except the core, which I like to thin-slice and stir-fry.
I made a fabulous blue cheese cole slaw last night. I used the whole head of cabbage (minus the core) and sliced it very very finely with my chef's knife. I also let it sit in the dressing for two hours before serving it to allow things to soften up a bit.