I had that happen once when the beets were picked late in the season and had gotten too large. I put them back in the kettle, recooked them to the desired doneness, reheated the brine to boiling and rejarred them. I always slice my beets unless they are smaller like walnuts, then I'll leave them whole. Piercing with a fork is usually enough to tell if they are cooked through, but as they are sliced you can also tell if they are cooked enough. I cannot imagine eating them raw as I don't like a strong "beet" taste, but that is just me. That's why I pickle them. haha