The problem with the statement “I’m entitled to my opinion” is that it's used to protect beliefs that should've been given up. It is a damaging element of public discourse for someone to say and think what they like, but you are somehow disrespectful if you continue to argue.
Ultimately, we are only entitled to what we can argue for.
There is a difference between opinion or common belief and specific knowledge.
Opinion has a level of subjectivity and uncertainty. It varies according to someone's tastes or preferences. (You like chocolate more than ice-cream.) It is pointless to argue about this kind of opinion.
If 'entitled to have your opinion' means everyone has the right to say what they want, the statement is true, but not necessarily important.
If 'entitled to have your opinion' means your statements are serious candidates for truth, then it's false. And this too is a distinction that tends to get blurred.
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