There are multiple examples of works of fiction using for their title a quote from another famous work: Aldous Huxley's Brave New World, Ernest Hemingway's For Whom the Bell Tolls and more.
The advantages are clear: by means of the quote, one can hint at the work's subtext, say something about the work on a meta level, stress a central theme. Invoking another work, one can summon a complex array of ideas, images and emotions using only a few words.
As an example, it would have been easy to think of For Whom the Bell Tolls as a distant story of some Robert Jordan - some individual entirely unrelated to me. But Hemingway tells us - no, you can't distance yourself in this fashion. You have no right. The tragedy touches every man.
Any mans death diminishes me, because I am involved in Mankinde; And therefore never send to know for whom the bell tolls; It tolls for thee. (John Donne)
Are there disadvantages? Any situations when I would not wish to use a quote from another work as my title, even though I have found one? (Finding a quote that says what I want, evokes the right ideas, and is also sufficiently recognisable to be effective, is of course a challenge, but one separate from this question.)