People have used fur for clothing for thousands of years, probably dating back to the Neanderthals, though its use as clothing diminished with the advent of woven fabrics. Because of its expense, fur has ranked as a luxury good and a desirable status symbol for hundreds of years. However, in many Arctic cultures, families will often pass down a fur coat for generations, due to the necessity for such items to keep warm.
Campaigns against the fur industry have been carried out for decades by animal welfare and animal rights organizations such as PETA, the Humane Society of the United States, and the International Fund for Animal Welfare.
Anti-fur activists argue that the killing of animals for fur is unnecessary and unjustifiable slaughter; is dangerous to wildlife population and distribution levels; and is a grave abuse of animal rights. Their campaigns have had some success in restricting the fur trade and reducing the appeal of fur products in some countries, although fur still remains popular elsewhere.
For fun, examine a fur-protesters shoes and/or belt. The anti-fur movement is much bigger and more vocal than the anti-leather movement, probably because it's much easier to go after rich women than Hell's Angels.
Ironically, in some cases using the right animals to make fur coats can actively help the environment. Conservationists in Louisiana have long encouraged people to buy fur products made from nutrias, which are an enormously destructive invasive pest wreaking havoc in the bayous.