The more emotional the belief, the less likely it’s true
Some beliefs are basically facts, but without absolute proof. Tomatoes are a vegetable. Tonight’s movie starts at 7:00. Then my friend shows me proof that tomatoes are a fruit and the movie starts at 8:00. Cool! I’m glad to be corrected.
Some beliefs make people really emotional. Think of one of your particularly strong beliefs. If someone showed you absolute proof that your belief is wrong, would you be glad to be corrected? Would you instantly change your mind? Why not? Maybe you see that belief as a part of who you are? Would changing it change your public persona? Your self-identity?
Some people, when challenged on their beliefs, get all upset and scream, “But I believe this deeply in my heart of hearts!”
Wow, look at all that emotion! It must actually be true! Yeah, right. As if the amount of emotion measures the truth of the belief. Maybe it measures the opposite. If it was absolutely objectively true, there would be no need to get upset. You could just point to the conclusive proof. That’s that.
Instead, you might be using that word “believe” to mean “my identity depends on this”. Especially if you feel the need to tell everyone your beliefs.
The problem, of course, is that objective, conclusive proof is not always available. We have to evaluate what evidence exists and form our own conclusions. I believe that my emotionally-held facts are true because I've amassed my own body of evidence. Of course, the person disagreeing with me has amassed their own body of evidence that they are right and I am wrong.
To use your own example: botanically, a tomato is a fruit. But botanically, there's no such thing as a "vegetable", so a zucchini (courgette) and a cucumber and a bell pepper (capsicum) and an eggplant (aubergine) and a green bean are all fruits as well. From a culinary perspective, we have chosen to classify certain things (roots / tubers, leaves, stems, and fruits) as vegetables because it's a useful classification. So I may see your friend's "proof" and still come away saying that a tomato is a vegetable (and also a fruit).
I don't think this invalidates your point that the more emotional the belief, the less likely it's true. But unfortunately the solution is not always to dispassionately go out and find the objective truth, because that truth may not be accessible or may not exist altogether. We must be comfortable living in the nuance.