Self loading rifles (firearms callable of firing a round, extracting and loading a new one by itself) are a very complex mechanical enterprise that requires high tolerances and advanced knowledge of metallurgy. There are a few thing you need for a self loader. Firstly you need a method of loading the next round which the nature of muzzle loading muskets made this task impossible, plus powder had to be loaded in separately from the round adding additional complexity to self loading. A magazine with a spring-loaded follower may seem obvious to you but this took time to develop. Many repeater rifles used tubular magazines in the gun which prevented the use of pointed bullets.

Another must is a strong receiver that can withstand high pressures. One shot produces a lot of pressure but automatic or even semi-automatic fire prevents the pressure in the chamber from having time to lower. This is why modern rifles use intermediate cartridges (7.62x39, 5.45x39, 5.56x45) and not the large beefy rifle cartridges of older rifles like the Mosin or Lee-Enfeild (7.62x54, .303); those cartridges produce pressure that too high for controllable, useful automatic fire.

Another reason independent from mechanical problems was the beliefs of most armed forces until The First World War. It was a common belief that soldiers with access to magazine fed bolt action rifles would fire wildly and waste ammunition. Now try to convince them that soldiers with weapons that load rounds by themselves are a good idea. Self loaders may seem like the obvious way to go but their development took a lot more then the simple idea of rapid fire weapons.

Sources T.L. McNaugher "M-16 Controversy": Skennerton, Ian "Small Arms Identification Series"

The main problem is the difficulties inherent in gunsmithing. You need some very precise metallurgy and engineering to produce a semi-automatic firearm, and mass-production requires a very advanced level of machining and metalwork to produce something that won't explode in your hand.

During the heyday of black-powder firearms, double-barrelled weapons were often used, and some manufacturers experimented with even more barrels, producing things like the Nock Volley Gun. However, these were expensive and required careful manufacture, which made them impractical as military firearms. Similarly, breech-loading mechanisms were developed, but they generally required hand-crafting and were delicate, meaning that they also could not be mass-produced. Further, black powder produces a great amount of byproduct, in the form of thick smoke and leftovers that can foul the workings of a firearm.

That byproduct was the main point preventing the development of semi-automatic weaponry after the widespread adoption of practical breech-loading rifles, although many models were produced. The development of 'smokeless' propellants around the close of the 19th century which produced a much smaller amount of fouling allowed the development of the mechanisms for practical semiautomatic firearms on a mass scale.