There are birds in the sky so why isn't the earth Bird shaped?
There are planets in the sky, so why isn't Earth planet-shaped?
Or is it?
The fallacy of your logic is the fact that you rely on Heavenly observations to prove your point.
How about the fact that the earth is flat? That water is flat? That the horizon is flat?
"Earth is Flat" is not a fact. "Water is Flat" is not a fact. "Horizon is Flat" is not a fact.
All three appear to be flat until you take into consideration longer distances or altitudes.
For example, select one spot near the end of very long coastline, next to water.
Weight hanging on rope will make rope be precisely vertical.
Horizontal is perpendicular to the rope line.
Select another spot on same coast line, 69 miles away.
New vertical is what rope shows There. Now horizontal is perpendicular to New rope line.
At distance of 69 miles new horizontal is tilted by one degree from old horizontal.
Measured by theodolite.
Google for "History of Geodesy".
Water also appears flat only on shorter distances.
Horizon also looks flat when you are low down.
And it seems to be always at the eye level.
But:
Every navigator will know how to use sextant.
And every navigator will know that they MUST include Apparent Horizon Dip into position calculations
when measuring angular elevation of Sun (at day) or well known star (at night).
https://en.wikibooks.org/wiki/Trigonometry/The_distance_and_dip_of_the_horizonWhen eye level is 100 feet above sea, horizon dip is 0.236 degrees.
Error of one degree converts into position error of 60 nautical miles.
So, error of 0.236 degrees will convert into roughly 14 miles.
If you were sailing for 100 miles, 14 miles can be an error of 7.9 degrees.
Older ships were sailing about 5-8 knots (5-8 nautical miles per hour),
and 100 miles is roughly 12 to 20 hours of sailing.
Accumulate this type of error during 8-12 weeks of sail over Atlantic,
and you will end up in Havana instead of Miami.
Doesn't matter if the Sun and Moon look like they do.
Doesn't matter to those who want to believe.
But it does to those who want to know, when pure belief is not enough.
Constant angular speed of the Sun from the observer shows it revolves around you, not around North Pole.
Constant angular diameter (apparent size) of the Sun confirms that fact, and shows that percentual change in distance from you to Sun is small.
Ancient Greeks weren't stupid. They were great in geometry.
They didn't care for religious beliefs, just wanted model that will work for real life activities.
You're assuming The Table is Plate shaped because of the dishes on Top of it.
So, he is assuming that the Earth is Disc because Moon and Sun are Discs.
In that case you are right for telling him he's wrong.