I try to quote only webpages that have links to scientific studies.
The refining process leaves white rice with very few essential nutrients. White rice is stripped of iron, vitamins, zinc, magnesium and other nutrients during the refining process. If you like the taste, great, keep eating it; but it doesn't help your health. Many people buy "fortified" rice: that means that the manufacturer has added artificial chemicals. I generally stay away from "fortified" things, chemicals made in a factory.
According to a study conducted by the American Journal of Clinical Nutrition, brown rice (and whole grains in general) are very healthy. http://now.tufts.edu/news-releases/new-study-suggests-eating-whole-grains-increases-metabolism-and-calorie-loss
White rice is associated with many diseases, like diabetes http://www.webmd.com/diabetes/news/20100614 And there are scientists trying to spread it into China, a country with high rates of diabetes. https://www.ncbi.nlm.nih.gov/pubmed/20656097
There are usually two objections to brown rice (and whole grains in general): arsenic and phytic acid.
It is true that rice (ALL rice) contains arsenic, and if you eat too much rice (like the Chinese do) you have high levels of arsenic. White or brown. Arsenic is a metal so it ends up in your feet and in particular in your toenails. Measure the arsenic in your toenails and it will probably be very high because of all the white rice that you ate in your life. If you always ate brown rice it would be a higher. (Arsenic is in the sea, so all fish contain arsenic, and most vegetables contain arsenic, so don't worry too much that you have high level of arsenic: everybody does, for one reason or another).
Brown rice also contains a lot more phytic acid... like all cereal grains! Phytic acid is simply a storage of phosphorus. The number one containers of phytic acids are nuts, followed by beans and lentils: precisely the food that you need to eat. https://www.westonaprice.org/health-topics/vegetarianism-and-plant-foods/living-with-phytic-acid Any whole wheat food contains a lot of phytic acid compared to white rice... that contains almost zero nutrients so also zero phytic acid. "White rice and white bread are low-phytate foods because their bran and germ have been removed; of course, they are also devitalized and empty of vitamins and minerals." If you eat beans, lentils or brown rice without cooking, yes you absorb this phytic acid that is not good for digestion. If you cook them at high temperatures in a proper way, much of the phytic acid dissolves.
But before you remove beans, nuts and brown rice from your diet, make sure of what you are doing. There are also experiments that show phytates help fight cancer and prevent heart attacks. "Those who consume more phytic acid are less likely to succumb to breast and prostate cancer." http://www.precisionnutrition.com/all-about-phytates-phytic-acid Same article: "Phytic acid helps prevent hardening of the arteries" (ie prevent heart attacks) "contains considerable phytic acid with a powerful anticancer activity" in https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3551059/
Brown rice is a good source of the aminoacids Tryptophan and Alanine, which are both important for the development of neurotransmitters, i.e. for your I.Q. :-) http://orthomolecular.org/nutrients/proteins.shtml