I'd just like to add that logic builds upon the rules of one's world. If these worlds are fundamentally different then it fails to be a way of reasoning or even communicating.
Logic is built on axioms but there are accepted axioms by almost everyone (mathematical and abstract ones like arithmetic for example). One don't want to contact someone who axiomatize something bizarre or insane (for example, saying 1+1=3, square=circle and even outside of the mathematics, saying "life is good for everyone"), no matter what one will say, they are sticking to these as axioms "beliefs".
Also you can build logic using "their" axioms and prove contradictions but it changes nothing. They'll dodge it and continue thinking what they want. They don't care about logic even using "their" axioms.
One can accept the differences in open and unsolved topics like God existence and afterlife, and its not limited to philosophy but each science and aspect (open problems have believers in each side).
But in topics like life and how its problematic, talking to these people who believe life is great is like talking to a wall. Telling you life is great and a gift while you are suffering and maybe in the verge of death. One is greatly suffering, where is the greatness? What is the gift? They won't answer. They'll omit logic (even if built on their axioms) and stick to the axioms themselves.
Sure some other people will use logic, but when they find a contradiction. They'll dodge like ones without logic