Do you also not believe in algebra?

Algebra is real, and like most all real things - requires no belief!

that are always consistently revolving around the same points regardless of viewing point on Earth, disproves the flat Earth theory.

Assuming this were true, and “the flat earth theory” were a real thing (it isn’t for the same reasons the “globe earth theory” is not a real thing), it would not disprove or prove anything about the shape of the world. It would establish (“proove”) the patterns in the sky! If you want to know the shape of something, you have to measure it!

We can all see and test this.

Agreed.

It does NOT fit into the flat Earth model.

I prefer the word “conception” - because there is no flat earth model (certainly in a scientific understanding of that word).

The only reason you feel this way is due to MANY other biases. Putting them aside, and just establishing that the shape and the motion of the sky are as you describe “proves” things about the sky! The inferences you make beyond that are simply that - unsound “leaps of logic”. Looking at the sky to determine the shape of the world is incredibly silly, and is only believed reasonable thanks to bias/influence from (the pseudoscience/religion/mythology of) astronomy.