I have to disagree that it's "intuitive" that the earth is flat.
Why?
We both look out from our windows. We both see what appears to be a flat earth extending for 100 metres, or maybe 10km.
Your intuition tells you that the earth is flat. End of story.
Initially, my intuition tells me the earth is flat. Logic then tells me there
could be an alternative to what I believe intuitively. I investigate further, and discover that there is an alternative—a spherical earth. I then check for the scientific evidence that points to the shape of the earth—be it flat
or round.
I discover tonnes of evidence for a spherical earth, but absolutely none for a flat earth.
I therefore conclude my intuition was incorrect, and the earth
is in fact spherical.
—Intuition can be described in one way as "knowledge or belief obtained
neither by reason nor by perception" and I think the flat earthers' "looking out their window" fits this definition.