Unfortunately, a lot of results (proofs) about infinities are counter-intuitive, and they can't be disproven simply by showing how they go against (your) intuit

Unfortunately, a lot of results (proofs) about infinities are counter-intuitive, and they can't be disproven simply by showing how they go against (your) intuition. A proof is not "someone else's opinion"; it is formal reasoning that stands on its own, apart from whatever opinion may have been held by the creator of the proof. In fact many proofs went against the opinion of the proof's creator. So, I'm not "scared"; I'm prefectly prepared to take a stand against unproven orthodoxies. But I have enough humility to realize that if I think I've found a contradiction in a proof by a great mathematician such as Cantor, and nobody else has found it, then it must be me that's wrong.