In this case, it means that you're not entitled to refuse to change a belief that's been proven wrong.

If you think "everyone likes chocolate ice cream", and I introduce you to my hypothetical friend Bill who doesn't like chocolate ice cream, you're not entitled to still believe that 'everyone' likes chocolate ice cream. You could still believe that 'most people' like chocolate ice cream, but if I was able to come up with a competent survey showing that 51% of people do not like chocolate ice cream, you wouldn't be entitled to that belief, either, unless you could point me to an even more definitive study that agreed with you.

Even the belief "I like chocolate ice cream" could be proven false in some situations - peoples' tastes do change over time, and you could try it one summer and discover that you just don't enjoy it any more.

It also implies that you're supposed to go looking for proof of your claims before you make them - that you're not 'entitled' to have or spread an opinion, but instead must earn the right by doing or referencing research.