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It is entirely irrelevant what the Church Doctors or saints or Popes have said regarding the shape of the earth.
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The authority of the Church does not extend to physical realities that can be determined by objective observation.
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The Church has no authority to define physical reality.

This is just a straw man.

The Church doesn’t define any kind of reality. The Church defines true propositions about that reality which have been revealed by God, and what constitutes a “matter of faith” is not limited to things spiritual or only “essential to our salvation” - that’s Modernist  tripe of the kind that makes a nonsensical distinction between something being “theologically true” and otherwise! - no, it includes facts concerning human history, the nature of man, and cosmology. If the Bible states that the dimensions of Solomon’s Temple were x,y and z, the the Church has the power and authority to infallibly declare in this matter.

“Objective observation”, by the way, is a contradiction in terms, and the notion that a “physical reality” - by which really meant a theoretical model abstracted from sense experience, thus based not only upon uncertain data but upon  projecting conceptual fantasies into that data in order to postulate the existence of a world lying behind the content of sense experience - the notion that this process - of the blind grasping in the dark for a cat that might not exist at all - could take precedence over divine assurance of truth is preposterous.


 

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The Church does not define in matters of irrelevancy to the Faith of Catholics.
You might as well look for a Church teaching on prime numbers or the volume of a sphere or the color blue.
If you want to play this silly game, however, then go right ahead, but it will never be resolved because it's based on nonsense.

"Flat" earth is complete balderdash.                    

I do not expect it to be resolved.  These people are clearly not open to changing their minds in response to better information.  I point out historical and theological errors of flat-earthers so that casual observers of this forum will not get the impression that it is usual for trads to believe the earth is flat or that the Church teaches the earth is flat.  Observers will see that such flat earth claims are met with disagreement based on strong arguments.

Is there some sort of bad history between you?  Or maybe it is a man thing that I just don't get because I am a woman.

No, there's no history.  Neil and I seem to agree on many/most issues.  And even on this issue I don't know if I disagree with him or not.  Except that I find the excessive emotionalism of his posts irritating.  He'll mock, taunt, and insult flat earth theory.  And many of the proofs he posts are only proofs if you believe them to be proofs due to confirmation bias.  So, for instance, the example of boats disappearing bottom-up at a distance.  I don't consider that to be proof unless one rules out other optical phenomena that could account for the observation.  I'm looking for hard-fast proof, and so far I've seen more attempts to do this on the side of the flat earthers, and most just rhetoric and mockery on the globe earth side.  Now, there's a lot of emotional rhetoric on both sides, but I'm talking about the "proofs" that remain after I sift out and discard the emotional content.