Why would I want to take immunosuppressive drugs?

To decrease immunity. Immunosuppresive agents are drugs that decrease immune function. While in most situations this would be undesirable, with certain conditions where the immune system is overactive or too aggressive, these drugs may be proper. Examples include to prevent rejection of transplanted organs, in autoimmune conditions to prevent tissue destruction, and in diseases with chronic inflammation like asthma.
To Attenuate... Your immune system in conditions which involve autoimmunity, chronic inflammation, or if you are a transplant recipient. This should only be done under the watchful eye of a physician.