About a week ago, we had a fascinating discussion here about when the states of the former Confederacy abandoned their sectionalism for support of the United States. I think the answer to your question is the same as the answer I gave there: The Spanish-American War.

There's a couple reasons for that, and I'd point you to Utley's Frontier Regulars: The United States Army and the Indian, 1866-1890 for some good explanations. First, the U.S. Army was drastically scaled down after the end of the American Civil War. There weren't many Southerners in the U.S. Army because there weren't many soldiers in the U.S. Army. As Utley points out, the U.S. Army's strength dwindled from about 55,000 in 1866 to less than half that figure by 1874. It remained that low until the 1890s.

Second, as a consequence of those low figures, there was little room for advancement. Many of the officers in the U.S. Army of the 1880s were the same officers that had enlisted in the Civil War as young men. John Summerhays, whose wife wrote one of the classic accounts of female military life on the frontier, stayed a lieutenant for 22 years because there were no openings.

As Utley explains, the U.S. Army after the Civil War remained the "Army of Sherman" long after that officer stopped serving as its top general in 1883. Sherman was followed by Sheridan (1883-1888) and Schofield (1888-1895), then Miles (1896-1903); all three men had served as general officers during the Civil War, though Miles only as a brevetted brigadier general during the fighting. Miles had a close connection to Sherman, however; he married Sherman's niece.

Naturally, it'd be difficult for a Southern man, young or old, to serve under the same leaders that led the Union Army during the war. Certainly, they could do it, and some did, but given the small size of the U.S. Army in the second half of the 19th century, there were other opportunities to be had.

Third, keep in mind that until 1876, the U.S. Army was effectively an army of occupation in many parts of the South. American soldiers, though few in number, were the de jure defenders of Reconstruction, the federal government, and equal rights. This meant they were in arms, fighting Southern men for as much as a decade after the official end of the war.

Now, let's circle back to the start, and talk about the Spanish-American War. When that war broke out, there was a call for a large number of volunteers, which meant there was finally great demand for new soldiers. Second, the officers that had led the Civil War-era U.S. Army were either retired or diluted by new men who hadn't served during the war. Third, Reconstruction had been over for more than a decade; the men enlisting as volunteers would have had no memory of U.S. soldiers occupying the South. All of the factors that deterred Southerners from joining the U.S. Army for 30 years were removed.