"Nobody cares what you think" is something they drill into you in law school, but sometimes I find myself wishing that it was taught to everyone, aspiring lawyer or not. Of course, much of the time it's used to correct the speech habits of students preparing for their first year moot, when prefacing any statement with "I think..." is just a bad idea anyway. But the true significance of this idea is subtle, and may take several years to sink in.
It doesn't mean that no one wants to hear what you have to say. It means that whether or not you believe what you are saying, and how strongly you believe it, is of no relevance. What your audience cares about is whether or not there are good reasons for them to believe it. In the practice of law, especially, your actual opinion doesn't matter, because you might well believe your client is probably guilty, but your job is not to decide that, but to advise the court as to the best arguments available for why there's a reasonable doubt.
I've had the opportunity to judge some junior high school debates, and find students very often falling into a similar trap. A speaker would stand up and deliver an impassioned speech starting out with "We strongly believe that the proposition must stand!" This is silly, because we know very well that in the next round, the very same speaker will be emphatically stating how strongly they believe the very same proposition must fall. And so the point here is the same as the one in law school: nobody cares what the speaker believes; we want to hear the arguments for why we should believe, preferable arguments we haven't considered before.
I was recently reminded of this lesson on a message forum I frequent. We had been discussing some topic or other, the death penalty, I believe, and had gone on for some five or six pages of posts arguing about whether or not capital punishment is cheaper than life imprisonment (it's not, when you take into account the appeals process necessary to make sure we don't execute someone innocent). And then, of course, after all this lengthy and thorough discussion, someone joins in posting his opinion that we shouldn't waste money on keeping these monsters alive in prison, and should just shoot them.
Obviously the poster hadn't read any of the thread, and was unaware or just didn't care that his arguments had already been presented and dissected in fine detail. No, he just wanted to tell us what he thought, sparking a new round of debunking the same old arguments. But why would anyone care to know that he, this anonymous person on the internet out there, happens to hold a particular and demonstrably common opinion? We aren't voting on it. We don't know him, we don't have any reason to be affected in any way by the fact that he holds or does not old that view. What we want to know is if there are good reasons why we should share that view. And if he'd taken the time to peruse the thread rather than boldly announcing his not-at-all unusual perspective, he'd know that the arguments he brought to bear were old news to the participants.
Now, it's not necessarily true that no one cares what you think. Some people probably do, and of course when we're voting on something, what each person thinks is aggregated together to give a result. And when you're planning a dinner party, it's good to know what each guest's culinary preferences are. But most of the time, it's a good guiding principle to bear in mind that the mere fact of your preferring A over B is of no value to anyone but you.