"Opinion: a view, judgment, or appraisal formed in the mind about a particular matter" - Mirriam-Webster Dictionary
Everyone has opinions. Frequently, one person's opinions differ from another person's opinions. Differing opinions regarding one's own preferences are natural and those differences contribute to the variety and spontaneity of life. I prefer red delicious apples, and my husband prefers gala apples. I have a compelling argument as to why I have such a preference, but the qualities that I find important and appealing may not be the same as the qualities my husband prefers. However, our disagreement on which apple is best doesn't result in either of us not getting what we would like. It just means that our fruit selection varies more than if we were to agree.
Some opinions apply to situations where not everyone will be able to get what they want. This happens with group events such as going to the movies, planning wedding menus, agreeing on a radio station on a road trip, and even things as serious as legislation. I can deal with having to listen to music I might not like, eating food that isn't my favorite, and seeing a movie that I might find less entertaining than another, but when opinion shapes legislation, I might be left with options that strip me of rights and resources. When having an opinion about what other people should or shouldn't be doing with their own resources and their own bodies is met with action, you should expect scrutiny.
"The greatest deception men suffer is from their own opinions." - Leonardo da Vinci
The more serious your opinion, the more anger or frustration you may feel at having your opinion challenged. You might also feel anger and frustration if, when trying to summon up a good reason for holding your opinion, you are reduced to shouting, huffing, eye-rolling, and other non-verbal behavior that signal your deteriorating emotional state to the other party. You may not have considered before that you could be wrong, and this possibility can be extremely troubling. You are good person, and you like to think that you do things for good reasons. At this point, you either have to insist that you are correct while attempting to skirt the issues of reason and evidence, scare off the offending questioner with threats or posturing, or concede that you may be wrong and wither away into a puddle of wrongness under some moldy rock amidst the muck and mire of the dregs of society.
"Opinion is the medium between knowledge and ignorance." - Plato
Everyone has been wrong, even overtly wrong in front of other people. It can be anything from mildly embarrassing to utterly crushing. But, realizing that you may be wrong is a profound state of mind, because it allows you to change. I am not saying that, just because someone disagrees with you, that you are wrong. But, I am saying that, if someone disagrees with you, listening to what they have to say and talking to them is important. Why do you think that way you do? Consider your own motivations and the points that the other person is making. What is important to them, and what is important to you, and why?
"Too often, we enjoy the comfort of opinion without the discomfort of thought." -John F. Kennedy
Frequently, opinions are formed out of an emotional impetus and maintained because we choose to see what supports our opinions and ignore what challenges them. One bad or good experience causes generalizations to be made that shape our perception of our environment. Additionally, people tend to choose company that share their opinions because it is easier to agree and remain amicable. Disagreeing with someone that you like can be uncomfortable, and even if two people may disagree about something, they might mutually decide to never discuss it by avoiding the issue. However, if nobody ever discussed their opinions, society would become static, dull, and unproductive.
Disagreements combined with mutual respect are important. Discussing important issues like politics and religion are important. Disagreements about religion and politics are unavoidable and have great potential for deepening understanding of each other as well as improving the standards by which we live as a society, so don't shy away from conflict. Temper it with patience and see what new ideas arise from not keeping your opinions to yourself.