In our friend, the dictionary, we find two main definitions of cancer: "a malignant and invasive growth or tumor" and "any evil condition or thing that spreads destructively" (source).
And would you know it? Fight Club deals with both.
Cancer is internal, affecting the mental (and obviously physical) health of a single person—and it affects almost every character in the book. Marla might have it. Big Bob had it. Our narrator almost had it, but it turned out just to be a birthmark. Being diagnosed with cancer forces each person to confront the inevitability of their own death.
But the larger implication of Fight Club is that humanity itself is a cancer. Deep, right?
Whether or not fight club and Project Mayhem are "evil" is up for debate, but they definitely spread destructively. They're a weird, contagious kind of cancer, spreading like, well, cancer, as our narrator flies across the country for his job.
And when our narrator realizes that he is Tyler (gasp!) and that he created fight club, he fears that "the cancer [he doesn't] have is everywhere now." (13.33) It looks like Project Mayhem has grown beyond the point treatment.