Vs the US, where there are loopholes that you can use to avoid even a basic background check, and then use it for the very first time to shoot someone.
Second, you learn a certain respect for the firearm and are expected to observe strict safety rules when handling it. That gives you a kind of psychological flinch when you consider doing anything out of the norm with it.
The difference might be in what guns mean to Swiss people vs. the US.
A gun in the US has this "if the government becomes destructive of these ends we can start shooting" connotation. A gun is there for self defense. Someone doesn't get off your law, you use your gun.
In Switzerland the gun and the compulsory military service you mention is there for the people to protect their country and fellow countrymen. You are trained in defending your neighbor, who just stepped on your lawn against outside aggressors.