It is a strongly held belief in America that "Everyone is entitled to his/her own opinion." After all, we live in a Democracy, and everyone should have an equal say. However, this assertion is fundamentally flawed when viewed from a rational standpoint.
As an easy example, if you were to say that "the sky is blue" and I were to say that "the sky is red with green polka dots," then you are right. It is an indisputable fact that the sky is blue. If I say that "it's my opinion that the sky is red with green polka dots," it does not change the truth. Rather, it is wholly disingenuous and underhanded of me to try and mask the truth using that phrase.
When "opinions" really become a problem, however, is when they are used as a final argument on controversial topics. Let's say, for example, that you and I are arguing about the safety of nuclear power. I believe that living within a few miles of a nuclear power plant makes me more likely to get cancer because radiation is dangerous. You believe that nuclear power plants are entirely self-contained and release negligible amounts of radiation. You then cite a study showing that radiation levels do not increase near nuclear power plants. In retaliation, I simply say, "Well, it's just my opinion that radiation is dangerous and living close to a nuclear power plant is bad for you." The fact that it is "my opinion" does not make it a valid argument; I am simply wrong.
Life is basically one big optimization problem. We want the most fun for the least amount of money, the most money for the least amount of work, the most enjoyment (or least displeasure) per unit of work, etc. As a rational thinker, your "opinion" should always be your best estimate of a given choice based on your available information. Since no one is omniscient, at least some of everyone's opinions are flawed. Therefore, when you cite the study on radiation, I should realize that you have given me new information, which I should then use to reformulate my opinion.
This applies to all opinions, even to the personal realm of beliefs and desires. You are the only one who knows what makes you happy; you are the only one who can view your utility function. Since no one else knows how much fun you find in video games or rock climbing, your opinion is the ultimate authority. Everyone else has zero knowledge on the subject. Yet, even in this case, listening to the opinions of others is worthwhile. Even though they do not know your utility function, others may propose ideas that you yourself had not thought of. This could lead to a better optimum allocation of time or money to yield maximum pleasure. After all, just because you've never tried rock climbing doesn't mean you won't end up liking it more than video games.
Refusing to re-evaluate your opinion after hearing new evidence is entirely irrational. In doing so you are likely hurting yourself by refusing to change from a sub-optimal course of action. If you are ever tempted to say "well, that's just my opinion" to refute an argument, take a step back and analyze yourself for bias. You are never "entitled" to your opinion; you are only allowed your best guess given your current knowledge. As soon as someone else comes along with a better guess or new information, you should change your "opinion" immediately.
This all boils down to one very important, rare, and difficult skill: admitting when you're wrong. If you can't admit when you're wrong, then you can't improve. If everyone in the world could freely admit when they're wrong, I think we could make some truly terrifying progress both scientifically and socially.
Based on this blog post of the same name.