@Cubist
I would not mind at all a question that asks “Can you find a relatively simple pattern that fits this sequence?” Pattern finding is an essential skill. What I object to is framing such questions in a multiple-choice format that implies whatever pattern X sees is the “correct” pattern.
I see a possible pattern. That calls for investigation, not dogmatism. I greatly doubt that you and I fundamentally disagree on that. I at least have developed hypotheses that turned out on further study to be wrong. Developing hypotheses is good. Recognizing indeterminacy is good. Investigating is good. What is not good is telling students that the student is wrong unless the student guesses what my process was when my process is not unique.
I am all in favor of intuition and creative hypotheses. What got me going in this thread was the implication that alternative hypotheses were excluded by the existence of one plausible hypothesis. I had to deal with too many fiascos created because people grabbed the first solution that solved some aspect of a problem. The last fifteen years of my career mostly involved dealing with problems that never would have arisen if someone had considered whether alternative solutions existed and which alternative was likely to be best under alternative futures.
We teach mathematics in part to teach thinking systematically. I love questions that ask what is possible. I hate questions that imply that an indeterminate answer is apodictically certain.
Ultimately, I suspect that multiple-choice answers, while convenient for grading, are bad for students because they imply a simple dichotomy between correct and incorrect that frequently does not exist.
