My immediate thought is "why is the equator warmer?"

Have em show how Antarctica can have a 24 hour sun on this model.

The real problem is that current flerfers have wised up to the fact that their model is shit, so most will say "we don't make claims/have a model we just point out flaws in the globe model."

The best way to demonstrate the earth curve is a water level sight though.

The problem would be that they've heard all of the common arguments against and probably be prepared for them. I would point out that this map has a pretty severe northern "hemisphere" bias that would make the age of exploration confusing. But I wouldn't be surprised to hear them say history is made up too

It's impossible for this map to have polar day or night. So bring them to Antarctica during the summer.

Ask them how long it would take to get from one side of Antartica to the other.

Why is there ice in the center and edge, with the warmest region being r/2?

Why are time zones shaped like pie slices? Like no seriously, show me a functional solar geometry that would give those observable time zones even remotely as well as the globe model?

Why do seasons flip at r/2?

i mean, "this goes against thousands of years of evidence, including observations you can make yourself" is a pretty good one