Why Does Oklahoma Have A Panhandle?

This meme isn't true. But the real story is interesting.

The Oklahoma Panhandle derives from one of those "how sausages are made" stories of the legislative process and the sustained fights in Congress over slavery prior to the Civil War. It started with the Missouri Compromise (requiring new northern states over a certain line of latitude to be "free states"). 

This affected the efforts of Texas to be admitted to the United States as a slave state, which gave rise to the Compromise of 1850 that had Texas cede the portions of its territory that violated the Missouri Compromise and tweaked eastern boundary of what would become New Mexico.

Also, the drafting of the Kansas-Nebraska Act of 1854 was sloppy. It really should have extended the Kansas border further South to the Missouri Compromise line at the 36°30' parallel north. A bill that passed by both houses of Congress, that was vetoed for some reason that isn't obvious by President Garfield in 1886, would have moved the boundary of the Kansas territory south to the Missouri Compromise line.

If this had been done, then what is now the Oklahoma Panhandle would very likely have become part of Colorado and not Oklahoma.

Wikipedia tells the story of how the Oklahoma Panhandle came to be:

The Oklahoma Panhandle (formerly called No Man's Land, the Public Land Strip, the Neutral Strip, or Cimarron Territory) is the extreme northwestern region of the U.S. state of Oklahoma, consisting of Cimarron County, Texas County and Beaver County, from west to east. 

. . .

The Western history of the Panhandle traces its origins as being part of New Spain. 

The Adams–Onís Treaty of 1819 between Spain and the United States set the western boundary of this portion of the Louisiana Purchase at the 100th meridian. With Mexican independence in 1821, these lands became part of Mexico. With the formation of the Texas Republic, they became part of Texas. When Texas joined the U.S. in 1846, the strip became part of the United States.

. . .

When Texas sought to enter the Union in 1845 as a slave state, federal law in the United States, based on the Missouri Compromise [of 1820], prohibited slavery north of 36°30' parallel north. Under the Compromise of 1850, Texas surrendered its lands north of 36°30' latitude. The 170-mile strip of land, a "neutral strip", was left with no state or territorial ownership from 1850 until 1890. It was officially called the "Public Land Strip" and was commonly referred to as "No Man's Land." The Compromise of 1850 also established the eastern boundary of New Mexico Territory at the 103rd meridian, thus setting the western boundary of the strip. The Kansas–Nebraska Act of 1854 set the southern border of Kansas Territory as the 37th parallel. This became the northern boundary of "No Man's Land." 

When Kansas joined the Union in 1861, the western part of Kansas Territory was assigned to the Colorado Territory but did not change the boundary of "No Man's Land."

After the Civil War, cattlemen moved into the area. Gradually they organized themselves into ranches and established their own rules for arranging their land and adjudicating their disputes. There was still confusion over the status of the strip, and some attempts were made to arrange rent with the Cherokees, despite the fact that the Cherokee Outlet ended at the 100th meridian. In 1885, the U. S. Supreme Court ruled that the strip was not part of the Cherokee Outlet. In 1886, Interior Secretary L. Q. C. Lamar declared the area to be public domain and subject to "squatter's rights". The strip was not yet surveyed, and as that was one of the requirements of the Homestead Act of 1862, the land could not be officially settled. Settlers by the thousands flooded in to assert their "squatter's rights" anyway. They surveyed their own land and by September 1886 had organized a self-governing and self-policing jurisdiction, which they named the Cimarron Territory. Senator Daniel W. Voorhees of Indiana introduced a bill in Congress to attach the so-called territory to Kansas. It passed both the Senate and the House of Representatives but was not signed by President Grover Cleveland. The organization of Cimarron Territory began soon after Secretary Lamar declared the area open to settlement by squatters. The settlers formed their own vigilance committees, which organized a board charged with forming a territorial government. The board enacted a preliminary code of law and divided the strip into three districts. They also called for a general election to choose three members from each district to form a government. The elected council met as planned, elected Owen G. Chase as president, and named a full cabinet. They also enacted further laws and divided the strip into five counties (Benton, Beaver, Palo Duro, Optima, and Sunset), three senatorial districts (with three members from each district), and seven delegate districts (with two members from each district). The members from these districts were to be the legislative body for the proposed territory. Elections were held November 8, 1887, and the legislature met for the first time on December 5, 1887. Chase went to Washington, D.C., to lobby for admission to Congress as the delegate from the new territory. He was not recognized by Congress. A group disputing the Chase organization met and elected and sent its own delegate to Washington. A bill was introduced to accept Chase but was never brought to a vote. Neither delegation was able to persuade Congress to accept the new territory. Another delegation went in 1888 but was also unsuccessful. In 1889, the Unassigned Lands to the east of the territory were opened for settlement, and many of the residents went there. The remaining population was generously estimated by Chase at 10,000 after the opening. Ten years later, an actual count revealed a population of 2,548.

The passage of the Organic Act in 1890 assigned Public Land Strip to the new Oklahoma Territory, and ended the short-lived Cimarron Territory aspirations.

Beaver County encompassed the whole Panhandle from 1890 until statehood. . . . "No Man's Land" became Seventh County under the newly organized Oklahoma Territory and was soon renamed Beaver County. Beaver City became the county seat. When Oklahoma Territory and Indian Territory were combined in 1907 as the state of Oklahoma, Beaver County was divided into Beaver, Texas, and Cimarron counties. 

The Oklahoma Panhandle had the highest population at its first census in 1910, 32,433 residents, compared to 28,729 in the 2020 census.