Essentially, because that's what the French, British, and Austrians mostly used. The 1855 Springfield and 1861 Springfield rifle-muskets were deliberately similar to French and British weapons. Switching weapon technology during the war was much more difficult.

In the years immediately before the Civil War, the U.S. Army was a deliberately small and underfunded institution. It's peacetime strength of 16,000 was tiny compared to most other countries. Accordingly, the U.S. Army looked carefully at European militaries as a way for a smaller military to stay at or near the cutting edge of technology and doctrine. U.S. Army officers observed European conflicts and took careful notes of European equipment and practice.

The last large conflicts in Europe prior to the American Civil War were the 1854-5 Crimean war and the 1859 Franco-Austrian war. These conflicts were fought (with the exception of the less sophisticated Russian Army) with rifle-muskets, muzzle-loading arms with rifled barrels which were an incremental improvement on smoothbore muskets. These conflicts maintained the French, British and to some degree the Austrians as the dominant military powers in Europe. American officers accordingly looked to imitate these powers, particularly France, in the matter of military tactics and technology. Accordingly, the U.S. decided to produce a rifle-musket of its own, the 1855 Springfield and its successor the 1861 Springfield which were quite similar to the French 1849 Minié rifle and British 1853 Enfield Rifle.

However, there was one European state which was ahead of other militaries in small arms. The Prussian army adopted a breech loading weapon gradually over the course of the 1850s following combat experience in an 1848-9 civil war. This Prussian Dreyse rifle or needle gun, although not technically a repeater, would prove the importance of increased infantry firepower in the 1866 Austrio-Prussian war. Yet the extent and importance of the innovation was not generally known in Europe in 1861, because for the most part the Prussian army was considered an untested military force of a smaller power and overlooked by European and American officers alike.

Once the American Civil War begin, Union and Confederate armies scrambled to grow at a rapid rate. The 1860 16,000 regular army would divide and increase nearly a thousand-fold to become a 1,000,000 man Union army opposing 500,000 Confederate troops by 1863-64. This process involved huge logistical exertions, political problems, and personnel issues. Just feeding these huge groups of people adequately was often beyond the ability of the governments and military organizations.

Although this process provided scope for experimentation in small arms, the sheer scale of it prevented any truly rational policy for re-arming troops with experimental weapons produced as a crash program. In 1863 a few small Federal units proved the value of repeating rifles in combat. Then only by 1864 did repeaters (Spencer carbines and Henry rifles) start appearing in moderate numbers, and only the northern states had the economic and industrial base to begin fielding them in anything like a systematic way. Both northern and southern militaries were too disorganized in period from 1861 to 1863, and by 1864 the Confederates were too economically devastated by the war to systematically re-arm to repeating rifles.