Can "the pill" cause gum disease?

Not Directly. Gum disease is caused by plaque...The sticky film of bacteria which clings to your teeth and invades the surrounding tissues. However, taking "the pill" can change your hormonal balance so that your gums are more susceptible to swelling, redness, and bleeding. This, in turn, can increase your risk of developing gum disease. Regular plaque removal and excellent oral hygiene are mandatory for you.
The Pill. Periodontitis is not caused by hormones or medications. If you have periodontitis, see a periodontist for evaluation and treatment.
NO. Birth control pill gives rise to the estrogen level, upon breaking down, resulting in production of estradiol, which acts as the growth factor for the prevotella gingivalis, one of the major periodontal pathogenic bacteria. This is more true with the case of pregnancy, resulting in "pregnancy gingivitis". However, the main etiology is still bacteria. Good oral hygiene will control this factor.
No. Gum disease is a bacterial infection. Birth control pills are hormone suppliments, ie estrogen. Although changes in hormone levels can increase the vascularity of oral tissues which are then more prone to infection (for instance when you are pregnant), this doesn't occur with birth control pills.