Just looking at a map, some places look like they’re gerrymandered district maps. When they were formed, what stopped western Oklahoma from being part of Texas? Northwestern Florida from being merged with Alabama? Western Tennessee from being a part of North Carolina (or vice versa)? Northern Idaho from being a part of Montana? Was it the same reason?
I would recommend reading How the States Got Their Shapes by Mark Stein, which goes state-by-state and details the hows and the whys of literally every border in the country.
The tl;dr of everything, of course, is politics. Each state you mention, though, does have a different spin based on the history and geography of the region.
Tennessee was a part of North Carolina's territory pre-America, and was given to the federal government when NC joined the US (or was supposed to; they did try their best to hang onto all of it). This served a few purposes:
The reason why the line is where it is, though, and why the strange jut between the states, comes down to the topography of the Appalachian Mountains, as seen in this map. The border follows the mountains; the mountains (a) made it difficult for those in the west to access the east and therefore have their concerns heard by the government there and (b) made the culture and lives of those on either side of the mountains very different, resulting in a lot of ignored and angry residents in the west (now Tennessee).
Florida's panhandle was actually much longer initially than what we know now. It extended along similar lines all the way to the Mississippi River when it was a Spanish territory. After the Louisiana Purchase, the US was concerned about access to the Gulf of Mexico, as we owned the western side, but the Spanish owned the east (again, all the way to the Atlantic Ocean). Additionally, in 1810, many of the settlers nearest to the Mississippi were American, not Spanish, and didn’t love being under Spanish rule. They staged a number of attempts to become part of the US, which were unsuccessful until James Madison announced in his second State of the Union Address that he was annexing West Florida to the Perdido River to keep the peace. This was very illegal, and Spain gets mad, sides with Great Britain in the War of 1812, which leads to the US battling in Florida and actually taking control of West Florida in 1813. Spain gets mad again, because they weren’t actually an active participant and this was another illegal land-grab by the upstart US, but they’re facing other issues that are more important that their American colonies and eventually just give us a ton of territory in the Adams-Onís Treaty of 1821, including all of Florida. At that point, we just left the rest of the geography alone, so the panhandle remains east of the Perdido River.
The tl;dr with Oklahoma’s panhandle is Texas and slavery. Texas joined the Union after the Missouri Compromise of 1820, which stated that no slave states could exist north of 36° 30´ latitude (except Missouri). In order to keep their slaves, Texas had to lop off everything north of that line. Later, the Missouri Compromise was repealed (and eventually found unconstitutional, per the Supreme Court’s Dred Scott decision), and the Kansas-Nebraska Act of 1850 took effect, which stated that territories could decide if they wanted to be slave- or free-states. When Kansas joined the Union in 1861, the southern border was set at 37° latitude and fell in line with the border between many other states (heading all the way west to the Four Corners and out to Nevada.) Oklahoma, then, basically just got everything in between those those lines of latitude. Because of evenness and nice lines as well as slavery policy.
Moving north, Idaho’s panhandle was decided mostly just by politics, although geography and topography again played a huge role. Sidney Edgerton was appointed chief justice of the territory of Idaho, but because of the oncoming winter, never quite made it to the then-capital of the territory, Lewistown. He stopped east of the Rockies, in Bannack, and was given the appointment of the eastern district, which very much displeased him as it was far removed from the capital and therefore the politics of Idaho. He later became the territorial governor of Montana, and was part of deciding where the division would be between Idaho and Montana (again, largely because of the mountainous divide, there wasn’t much/enough oversight in what is now Montana). One proposal was the Continental Divide, but Edgerton argued for a border following the Bitterroot Mountains (which gave Montana significantly more land). Ultimately, the Bitterroot Mountain line won out except in the northern panhandle, where a little bit was lopped off and given to Idaho because it held valuable agricultural land, and Idaho didn’t have a ton of that at the time.
I hope that’s sourced enough for r/askhistorians - I think the history and borders and geography of the US is fascinating, and I did learn a ton from Stein’s book, which is a really fast and pretty easy read. Enjoy!
For the case of the Oklahoma panhandle, Texas was required to relinquish that strip of land when it joined the United States because, under federal law as a result of the Missouri Compromise, a slave state had to be located south of 36°30' parallel north. Therefore 36°N30' forms the southern border of the Oklahoma panhandle. Texas surrendered this land in the Compromise of 1850 and it remained officially a "Public Land Strip" not belonging to any state or territory from 1850 to 1890.
This Compromise of 1850 also defined the eastern border of New Mexico Territory as the 103°W meridian, forming the western border of the future panhandle. Then in the Kansas Nebraska Act of 1854, the southern border of Kansas was defined as 37°N, forming the northern. The strip was later assigned to Oklahoma Territory by the Oklahoma Organic Act in 1890.
There's a bit on some jogs, most notably Oklahoma's panhandle, in this thread here that you may wish to peruse. I had to use Google to find it because Reddit's search function is, well, you know. I link to my own response in there about the two-mile shortfall in the widths, which you'd expect to be the same if the Missouri Compromise line were the thing. There are a lot of reasons, but intersecting legal complications (governmental and private alike!) and plenty of survey errors in the first 150 years of the US's existence are fairly prominent among them. There is no doubt much that can still be added, but a number of book suggestions in the general thread I link above are still very good places to investigate too.
