I know I've heard someone give some quote from a general about this, but for the life of me I can't remember who it was or when. I can't track down a source. I know that there were similar biases against automatic weapons later in history because they would waste bullets (one WWI Field Marshal called the machine gun "much overrated"). Help me /r/AskHistorians and thanks in advance!
General James Wolfe Ripley, the Army Chief of Ordinance had no use for breechloaders and repeating rifles and considered them "newfangld gimcracks." Specifically he thought that repeaters would encourage the waste of ammunition.
At the time of the Civil War, there were several breechloaders and repeating rifles readily available, and all saw service to one degree or another. The Sharps carbine for instance was widely popular with the cavalry, and along with the Burnside carbine, and the Spencer and Henry repeating rifles, were among the most common breechloaders of the war.
The problem with General Ripley, is that he was able to bypass President Lincoln's order in 1861 to acquire 10,000 Spencers. Because he answered to Secretary of War Edwin M Stanton, Ripley could drag his feet, and block the procurement of the weapons, which he did until forced by Lincoln to move faster. Even then, Ripley managed to delay and slow down production and acquisition of Spencer rifles.
The New York Times gives a very nice write up on the issues behind adopting breech loading and repeating rifles at the time.