Snagged
” Chatzos is when is at the highest point in the sky, which is exactly halfway between sunrise and sunset.”
the first half of your statement is true not the second.
chatzos is when the sun is at the highest point in the sky this is known as “solar noon”
See Ig”m EH Chelek 1:58 where he gives real examples for example on 4/20 Haneitz is at 5:10 while shkiah is at 6:40 the midpoint is 11:55 yet chatzos is 12:00 making the 6 morning Shaos zemanios slightly longer than the 6 afternoon shaos zemanios. This is what Halevai was reffering to in his OP
If your second assertion was true then chatzos would take place at exactly the same time every day. since it takes 24 hours for the Earth to spin on its axis. So if the sun is at its highest point at 12:00 (regardless of when sunrise/sunset take) place 24 hours later it should be back in the same place. Which while close, isnt the case. however to to the elliptical orbit and the tild effect among other factors their is some slight variability) though I dont understand R’ Moshe who seems to say Chatzos is always at 12:00