South vs. North in the US is determined by history as much as geography. It all goes back to the US Civil war and the slavery issue.
Look at this map:
The states in red were the states that seceded from the US in the Civil War. The light blue ones (Missouri, Kentucky, West Virginia, Maryland) were states where slavery was legal before the war (like the rest of the southern states) but they didn't secede from the Union (like the northern states).
Texas is a bit of a unique case because it was a Confederate state, but culturally has as much influence from Mexico and the western US as it does from the rest of the South. That's why people like Dewi say "Texas is not the South." It depends who you ask and what they mean.
Anything west of Texas isn't considered "The South" regardless of latitude, because 1) they were territories, not states, and 2) there was no slavery there.