Why do I have to have the other side of my thyroid removed?

So I got my test results for a thyroid nodule that was removed with the left side of my thyroid a couple of weeks ago and the doctor says that it is papillary thyroid cancer. The doc also took out some lymph nodes and they were all negative for cancer, so it looks like its confined to the thyroid (and just that lobe I'm hoping). My question is, what happens if I leave the other half of my thyroid and do not do the iodine treatment? Is this even an option? My doctor says that I could do that but that he recommends I just remove the other half, but I REALLY don't want to do that, at least not anytime soon, so can I just do nothing for now and hope that all the cancer is gone?