There's a lot of controversy surrounding shooting games - Duke Nukem was blamed for a shoot out in a cinema while countless others have been accused of poisoning the minds of youths and making them more likely to participate in gun crime. Despite the controversy however, they remain one of the most popular genres with only driving games and fighting games coming anywhere near to toppling them. Even those games that are mostly focused on exploration (such as Tomb Raider) or theft (such as Grand Theft Auto) often still have elements of shooting in them.
So what is it that makes them so appealing to young folk? Well really, it's not at all a new phenomenon and it can be found just as readily in other genres. Take films - the action genre is by far the most popular with all the big budget summer blockbusters falling into that category. Almost every single one of these films involves guns and could be described as 'shooting films' and really computer games are no different.
The purpose of a computer game, like most other entertainment, is escapism. People who play computer games want to feel cool and have adventurous lives. They want to mimic their superhero idols, be space heroes from the future, try being a cop in a dangerous part of town, or being on the other side of the law... they want to be pirates, soldiers, and rebels without a cause. In short, it's much more exciting to walk casually out of an explosion with a shotgun over your shoulder than it is to be a school teacher or learn knitting patterns. And why is that? Because you can do those latter things in real life! If the games want to stay realistic then they need to involve guns. The other reason that's more exciting obviously is the higher stakes - if it's a matter of life or death then that's more exciting than winning a gold or silver medal... and guns certainly facilitate this. In short shooting games enable a player to feel 'cool', feel as though they're taking part in an action film, feel a rush of adrenaline, and experience something they've never experienced before while remaining fairly realistic.
Shooting games also have a number of other advantages on top of their escapist appeal. On top of the cool factor, shooting a gun also requires fast reflexes and good special awareness to aim. These are two elements that lend themselves very well to the gaming experience and add an element of skill and challenge. This is also far easier to mimic realistically than a fighting game as the controller can make a great replacement for a firearm but not really the entire human body. When you shoot a gun you're pulling a trigger, and when you're using a controller you're pulling a trigger or pressing a button - the translation makes good sense. While shooting games involve skill, they also involve tactics and quick thinking - shooting an explosive barrel to take out an opponent, or smoking them out with a grenade while you get cover behind a nearby wall. This mixture of tactics and skill is something that isn't really found in other game genres (football or point and click games are tactical while driving or fighting games are more skill). This not only makes them a fun challenge for the user but also means that they're developing those skills - improving hand eye coordination and the ability to make quick decisions.