Hi Moach,
The reason why you would carry the launcher or any other shoulder fire weapon on the opposite shoulder is it will interfere with you placing your rifle to your shoulder to fire it. Also in real world combat the weight of the launcher would pull your shoulder down and cause you to fire low and to the right of the target you are trying to shoot at. If you are on patrol and come under fire the first thing you would do is find cover and take the launcher off your shoulder so you could move easier under cover, and then return fire. You can pickup the launcher if you move or need to use it. In the game you are given a freebie and you can fire standing, kneeling or prone with the launcher never interfering with your movement or firing your weapon. I'm left handed in the "real world" and would carry everything opposite of everyone else. So I was always hitting someone with my rifle barrel in the head. Or while on the range during training I would have to use firing point #1 or I would end up with hot brass cartridges hitting my neck, and several times going down my shirt. The animation is correct for a right handed solider carry a launcher.

Note: I spent 6 years in the US Army 68mike and then 16 years in the US Air Force as a CATM Instructor. That is a Combat Arms Training and Maintenance Instructor/Range Master. I'm very familiar with both US, NATO and Foreign weapons, how to use them, repair them and of course carry them.

I don't even see how you could carry a NLAW on one shoulder like that. It would fall of constantly.
In FDF we're simply taught to carry it across the body on left shoulder with the nose pointing down.
It doesn't get in the way of your rifle and to take it off your back you simply swing it around to your right arm and push the clips in to release the strap.
Example in these pictures http://www.puolustusvoimat.fi/wcm/a09eb4804fb6dd9c9431b700a50fdfac/1/kuvitus-7924.JPG?MOD=AJPERES&CACHEID=a09eb4804fb6dd9c9431b700a50fdfac/1
http://www.army.mod.uk/images/central-panel/fusilier_and_nlaw_502x335.jpg

Cool! I figured there had to be a good reason for that -- Kudos to BIS for getting that right then! :D

Another reason is a game-technical one: sometimes your character puts the rifle on its back, for instance when using binoculars or pistol. The rifle goes on the right side which would interfere if the launcher was there.

So in the game you have 3 visible weapon slots, rifle on the right, launcher on the left and pistol on the leg.

Even though Arma3 looks very realistic sometimes, these weapon slots are the result that the Arma soldier is still a computer guy which needs some simple places to put stuff without these things clipping (visually overlapping) or using complicated weapon sling simulations.

It nice to find out though that launcher-left is realistic as well for r-handed people.