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The argument for the skyline being a refraction or a mirage does not prove a curved earth it merely assumes a curved earth....
Nobody is saying that the refraction effect is evidence for curved Earth. You raised the fact that sometimes one can see Chicago from far away as an objection to the global earth idea, and it was explained to you why and how that happens. It is a non-issue.
What is an issue is that you haven't dealt with many proofs of the global earth, motion of the sun, the way objects are generally not visible far away, that you can see further if you are higher up, sunsets, the size of the sun staying the same during the day, and a whole set of other facts, that you deny, ignore, change the topic or "will consider". Then you have the gall to explain to us how you are having a "debate", and how it works.