Mark Goodacre gives ten reasons to question "Q".
I think the best answer when someone asks if you believe in Q is to answer "yes." Then when they astonishingly question if you are putting them on, simply reply:
"Of course I believe in 'Q'. 'Q' is Matthew."
I apologize to those who are not into Biblical Criticism and may not know who or what "Q" refers to. It's probably best to stay that way! But for those who are interested:
"According to the Two Source Hypothesis accepted by a majority of contemporary scholars, the authors of Matthew and Luke each made use of two different sources: the Gospel of Mark and a non-extant second source termed Q. The siglum Q derives from the German word "Quelle," which means "Source." Q primarily consists of the "double tradition" material, that which is present in both Matthew and Luke but not Mark. However, Q may also contain material that is preserved only by Matthew or only by Luke (called "Sondergut") as well as material that is paralleled in Mark (called Mark/Q overlaps). Although the temptation story and the healing of the centurion's son are usually ascribed to Q, the majority of the material consists of sayings. For this reason, Q is sometimes called the Synoptic Sayings Source or the Sayings Gospel. Some scholars have observed that the Gospel of Thomas and the Q material, as contrasted with the four canonical gospels, are similar in their emphasis on the sayings of Jesus instead of the passion of Jesus." [Source]