Simply put, it's because of the Revolution. Before the Revolution, recruitment was limited to contracts given to recruiters to recruit an X number of men for which they are paid. The horror story is of civilian men being made drunk by generous recruiters and wake up in the barracks (see Candide) or generally they would be pulled into the service by a lust for adventure and action (as many to be Marshals of the Napoleonic Wars did, several serving as Sergeant Majors before the Revolution).

The change happened when the threat of to Monarchs of Europe decided to try to squash the Republic in anger for the "murder" of Louis XVI. So, as lot of soldiers needed to be recruited and thus mass conscription was brought in to help with troop numbers. (My Rousseau is a little rusty but I believe that he advocated for mass conscription so that everyone helps in the defense of the Nation)

In other nations, there was still fear of rebellions and uprisings that would make it inadvisable to give the common people weapons and military training. It was so prevalent in Austrian thought that they even had thousands of combat capable troops scattered across the Empire despite being attacked by Napoleon in 1809, I believe at least a quarter to a third of the Austrian Army was needed to keep a presence and Archduke Charles always advocated a defensive strategy to ensure that there were troops to protect the crown lands.

If there is any single reason, it's because the Crown didn't trust the peasantry with guns.