In the world of carrying a handgun, everything is subject to change. One of the few fundamentals that remain constant over time is the concept of carrying your gun on your stronghand side so that it can be drawn with your (wait for it) strong hand. Well, that is of course, unless you use a crossdraw.
So put yourself in a time machine and let us go back to the 1850s. Revolvers were new-fangled items but those sold in a caliber large enough to do damage were huge. For instance, the 1851 Colt Navy, a .36-caliber cap and ball six-shooter, weighed 42-ounces and was 13-inches overall-- and it was not the longest revolver on the market by any means. For comparison, a full-sized K-frame Smith and Wesson 38 of today comes in at 30 ounces and 9 inches overall.
With such beefy and outsized revolvers, if you wanted to carry one of these so called new 'belt pistols' on your person the best way was in a crossdraw fashion in which the holster was mounted on the offhand side (e.g. left side if right handed) with the butt forward so that it could be drawn across the midsection with the strong hand. These guns were simply too long to pull out of a holster located on the belt directly under the strong hand, especially if mounted on a horse.
The crossdraw was standard until shorter cartridge revolvers like the Colt Peacemaker came on the scene in the 1870s. Still, for huge long barreled revolvers such as the S&W Model 29 and the Colt Python, the crossdraw remained in use with law enforcement officers as late as the early 1980s for the same reasons as in the Civil War-- it was just more practical.
Problems of the technique
Today the crossdraw is rare in both law enforcement and in personal defensive carry. The largest segment of the population that uses this technique is the cowboy action shooter hobbyists and civil war reenactors who carry reproductions of the same guns that pioneered its use to begin with.
Probably the worst thing for concealed cross draw carriers is the fact that almost any technique where you draw your handgun is going to require two-hands: one to pull away the jacket or coat and one for the weapon. Bigger guys and girls with a good-sized belly will have issues reaching across unless the gun is carried more in the 11 or 1 o'clock positions.
Shoulder holsters by definition, are crossdraw, but like the 1970s and the era of the six-inch S&W service revolver for law enforcement, their time has peaked. There are only so many carry options for shoulder rigs (sports coats, roomy rain jackets etc.) that don't print excessively unless you go with a small frame gun.
Upsides of the cross draw
(For large hunting handguns, a popular method of carry is the cross-chest harness holster such as the one shown. Its a modification of the old cross-draw US Army Tanker holster, but it works well)
Now dont get me wrong, there are those who prefer the crossdraw and carry as such every day. If you are in a seated position, in either an office chair or automobile, the crossdraw is a near ideal method of carry as it puts the butt-forward and within easy reach while seated. Remember this is why the old horse soldiers carried their Colts and Remingtons crossdraw fashion in the first place.
Officer Jim Ritter uses a fully restored 1970 Plymouth Satellite police cruiser as his everyday cruiser. And the vehicle is attracting attention on the streets of Seattle. He also wears the 1970s Seattle PD uniform complete with service bars and a crossdraw S&W.
While many standard holsters can simply be rotated around to the offhand side for crossdraw carry, a number are specifically made to take into the change in cant to place the grips flat against the body and within quick ergonomic reach. This has the bonus of allowing a draw from the offhand, which is usually not the case if carrying strong-hand only.
With proper training and a good bit of sweat equity put into practicing your draw stroke to where you minimize muzzle flash, the crossdraw can be fast and efficient.
Even for a 175-year old technique.