You know the old joke: "Why do Jews have short necks?" Followed by a deep shrug of the shoulders, the head sinking between them.
Rabbis respond to questions with a shrug quite often – I certainly did in my pulpit years - but the rabbinic shrug conveys different messages, depending upon the context. Here are a few examples of possible meanings, but I'm sure there are more.
A. "That would be a really long discussion, and I don't have the sources/time right now, so I'll leave it with 'I don't know'"
This isn't meant to be rude, it's just a recognition of reality. Hopefully, the Rabbi will come back later with sources, since disappointing a congregant who wants to learn would be criminal. [Case in point – my exchange with bratschegirl here, which was the trigger for this post.]
B. "That has no resolution"
Sometimes the questioner has a very good point, but we still don't accept his point of view.
Questioner: Praising Pinchas encourages zealotry!
Rabbi: This is a very good point – but we still praise Pinchas.
Rabbi: Because zealotry is an important value in certain situations.
Questioner: But most real-life cases involve the wrong situations!
C. "I have a personal view, but that does not require a psak."
As the Rambam said regarding purely philosophical eschatological issues, we have no need to issue halachic rulings in certain areas. So why do it? [But see "A" above – the rabbi certainly should offer to discuss the various views.]
D. "There is another way to look at this, but there is no way that you would accept the second side if I would present it, and it would only result in you being angry with me, so I'd rather leave it be."
I can't count how many times I have gotten into trouble by explaining a point of view with which I didn't agree, just for the sake of being honest about both sides in a given issue. No matter how extensive the disclaimer, people tend to assume that you sympathize, at least on some level, with the view being presented. On issues like Talmud study for women (I endorse it where it is done seriously and for students who do want to learn it - just for the record), for example, it can be safer to shrug than to explain the opposing point of view.
I'm sure there are other meanings for the Rabbinic Shrug, but that's all I have time for right now. It's a classic Type A case -
"Rabbi, aren't there other meanings for the Rabbinic Shrug?"