The problem with “I’m entitled to my opinion” is that it’s often used to shelter beliefs that should have been abandoned. It becomes shorthand for “I can say or think whatever I like” – and by extension, continuing to argue is somehow disrespectful.
This attitude feeds into a false equivalence between experts and non-experts, it makes people feel that they can weigh in on issues we know nothing (or very little) about.
This attitude helps people defend saying things like “you don’t look it”, when they find out that someone is disabled , has an invisible illness or is of a different ethnicity. When really what they should be saying, “I didn’t realise”, thereby acknowledging the difference between experts and non-experts (and to which of those two groups their opinion belongs to).