I think not having facts is a pretty big problem (but those facts have to come from reliable sources, saying you have facts and then presenting an anonymous post from /pol does not count as actual facts), but in my opinion the biggest problem is not being able to change your opinion based on newly discovered facts and different points of view. Some people see statistics and facts that prove them wrong and still are too stubborn to accept them. But again, one study isn't enough evidence (case in point, that one fabricated study about vaccines that all the anti-vacs build their arguments on), maybe there are 1000 other studies that conclude the opposite, which is why it's important to look at multiple sources and from multiple angles.
And my personal mantra for argumentation: Personal experience is NOT evidence. (Present it if you want but only as an example to go along with actual proof, because personal experience differs from person to person and therefor cannot be counted as actual evidence.)
But I'm curious, what do you think is the biggest problem?
But I'm curious, what do you think is the biggest problem?