If something is getting between the sun and moon, both of which we can track and accurately place in the sky at all times from earth, then for an object to cast a shadow on the moon has to be directly between the sun somewhere, which should be easy to track too since it'll be a linear line. The problem here is for something to cast a shadow it has to block or reflect the light from the sun, which would mean it would be visible or clearly blocking anything behind it from our view, so in theory we could see the shadow object in the sky (or just not see behind it, which would still make a visible effect in it's place).
If we should clearly be able to see the object then why has no one seen it yet? And if it does not exist as far as we can see, then surely there must be an object we can see that is causing the shadow instead, which would be the earth in round earth logic, since we can accurately track and predict the earths movements around the sun and the moons movements around the earth in this method.
Why do you think we should be able to clearly see the object? It's orbiting the sun, the brightness of the sun drowns it out. You can't see the stars during the day can you? Why would you be able to see an object that doesn't produce or reflect any light?
First, With that logic how can you see the moon during the day? Heck how can you see anything during the day if the suns light 'drowns' everything out visibly? The sun emits light, which travels and bounces off surfaces and into our eyes, without the sun we cannot see anything.
Second (but not important), you can see some stars during the day.
Third, this object would theoretically somehwere between the moon and the sun so it'd need to be big enough and pretty close to the earth so it'd be a pretty big, close object which we'd be able to see.
fourth if it's somewhere between the sun and the moon then what's to say we can only try looking for it during the day time? The lunar eclipse happens visibly at night after all.
fifth, lets say there's the possibility the this object is right next to the the surface of the sun and it's pretty tiny, it's still going to be visible when we look or around at the sun (through filters obviously otherwise we'll go blind).
It would definitely be visible in the sky to us, either by eye or by magnification (telescope) and since no one has found or seen it yet, how can it exist? How is it possible that people use such logic against round earth by saying "no one has seen the earth being round, I haven't seen it with my own eyes, I can only visibly see flat surface so it MUST be flat" while also saying "there's an invisible object in the sky no one can see that somehow still casts a shadow despite being totally invisible".
I guess, why is it plausible to have a magic invisible yet solid object in the sky that no one can see that causes lunar eclipse yet completely implausible that the earth is between the sun and moon causing the eclipse? Something proven by maths to be the case if the earth is a spheroid orbiting the sun.