To some people, facts and critical analysis don't matter. What matters to them is twisting facts to fit the narrative they're interested in.
Have you seen Tom's posts? That is literally his jam.
It's unfortunate that you have been bombarded with people sending you this picture with "check mate, flat earthers!" type messages from RE people, just as it is unfortunate that you see so many "The horizon is flat, check mate, round earthers!" type comments on the internet from FE people. And as I've highlighted to you recently, your own FAQ contains this kind of reasoning:
The evidence for a flat earth is derived from many different facets of science and philosophy. The simplest is by relying on ones own senses to discern the true nature of the world around us. The world looks flat, the bottoms of clouds are flat, the movement of the sun; these are all examples of your senses telling you that we do not live on a spherical heliocentric world. This is using what's called an empirical approach, or an approach that relies on information from your senses.
And yes, I've seen the first sentence, you're not claiming this is the totality of your evidence but I would suggest if you're interested in critical thinking it should be no part of your evidence or argument.
"The world looks flat" isn't evidence of anything other than the earth is large.
"the bottoms of clouds are flat" isn't even true
"the movement of the sun" is more evidence that the sun goes round the earth rather than the earth rotating but that is more a heliocentric/geocentric argument, not a shape of the earth argument.
I agree with what you're saying, but neither FE or RE has a monopoly on stupids or people who can't think critically.
And yes, it is unfortunate that this sort of thing extends to the media, that - and the sheer amount of nonsense on the internet - makes it even more important that kids are taught to think logically and critically.