Who gets to decide for everyone else what the "obvious truth" is and what the "dumb ideologically driven belief" is? If the truth or falsity of some point is in contention, then the way to resolve the disagreement is to allow all sides to argue and justify their position. Of course this system doesn't always come up with the right answer, but no magical infallible truth-determining oracle exists, so we do the best we can.
Under certain definitions of "1" "2" and "+", 1 + 1 = 2. But it's completely possible to define mathematics where 1+2 doesn't equal 2. It just so happens that we have a universally-shared convention on arithmetic.
But that simplicity quickly breaks down when people don't share the underlying axioms, and "fact checking" regularly operates in that space. For example, does 1+1 = the number of human genders? Everyone where I'm from would say that's an obviously true fact, but a lot of the folks who run Twitter would disagree.
