File under the list of famous people believing stupid things: this interview of a basketball player in which he refuses to say that the earth is round, instead asking a bunch of questions about how we can prove it's round and talking about how irritated people get with him for questioning it.
So first, in the spirit of this XKCD comic: Yes, I can quite easily prove the earth is round. It's why objects traveling over the horizon disappear from the bottom up - something that anyone can go see for themselves by going down to a shoreline and watching ships sail away. The last thing you'll see is the ship's mast (although you'll probably need a decent pair of binoculars to get a good look). Even if you don't happen to live near a shoreline, you can run the same experiment yourself with any large flat area and a tall object - once you get far enough away from the tall object you've chosen, you'll only see the top of it. At that point all we need is a simple picture (not to scale, obviously) to show that this is what we'd expect to see if we live on a ball and there's our proof.
But there's a larger point to make about whether this sort of discussion is a good use of our time. I'll grant that it forces people to ask questions that help educate everyone around them, so there is some benefit to be found, but I'd still argue that it's not all that helpful. It doesn't help us discover anything new, it doesn't help illuminate what we do and don't value (or how we'd rank the things we value against each other)... it's just a simple "oh, you don't know this answer? Here it is".
Which is useful to some people, and we need to react to people in a way that allows them to ask the question in the first place. However, if that answer isn't acceptable, and the questioner wants to continue the discussion, at that point it is perfectly fair to ask them to produce reasons why the initial answer isn't sufficient - and to criticize them if they are unable or unwilling to provide good reasons. And the initial answer being a bit obscure or counter-intuitive at first glance is not generally a good reason.
One of the comments in that interview is "Does it really bother you that much that I think something different than you or that I actually want to have that conversation?" My answer is - if you don't have anything useful to say, then yes, it does bother me, because that's not a helpful discussion to have.