M_A_M,
Good luck with your article. I think you came to the right place for help. Here are my answers to your questions:
Why is this rifle so popular?
They are popular for a laundry list of reasons. Probably the single biggest reason is that they are "cool". If you grew up watching action movies or playing video games, the AR-15 was probably the hero's weapon of choice. If you are mechanically inclined (or even want to be, but aren't), they are a complex enough mechanism to be fascinating, while simple enough to be within reach of Joe Everybody. They are the most modular firearm ever, and are completely customizable by the user. Why are custom cars popular? Or custom motorcycles?
They're also cool because America's "good guys" use them. In one form or another, AR-15's have been standard issue for the military since the 70s, and are the current long-arm of choice for law enforcement too. I think it is important to note, however, the AR-15 is not a civilian version of the M16 or M4. The M16 and M4 are configurations of the AR-15 adopted for military use.
Probably the second biggest reason AR-15s are popular is that they are fun to shoot. They are ergonomically simple to use and easy to learn. They are accurate (shooting is no fun if you can't hit what you're aiming at). They recoil more than a .22LR (I'm not a macho, big-caliber guy, but I personally find .22LR to be a bit boring), but are soft enough to comfortable for everyone. Standard capacity 30-round magazines mean you spend more time shooting and less time reloading.
You could write books on why the AR-15 is great, but I think those are probably the two biggest reasons people buy them (outside of the current political scare).
Obviously not designed "to kill as many people as possible", can you say what the design goals were (or point me to a link)
Working for ArmaLite, Eugene Stoner first designed the AR-10, the AR-15's bigger cousin, as a lightweight infantry rifle in 7.62x51mm to compete in the bid process that ultimately led to the adoption of the M14 in the 50's. When the Army started looking for a lighter weapon in an intermediate cartridge to match the tactics that were being adopted in Vietnam, ArmaLite proposed the AR-15 and won. The AR-15 was designed as a simple, lightweight rifle chambered for an intermediate cartridge. Smaller cartridges in bigger magazines meant that soldiers could carry more ammo. For the same weight of ammunition carried, soldiers could lay more suppresive fire.
The attributes that make the AR-15 a great infantry rifle are the same that make it a great civilian rifle, whether your purposes are sport, hunting, or lawful self defense. It's light, accurate, and shoots a soft recoiling cartidge.
Why is the AR-15 the poster boy for gun control?
The AR-15 is the villain of the gun control lobby because it looks scary. That's it, plain and simple. There are plenty of other rifles that have the exact same function, but don't have that military look. Unlike past generations, the overwhelming majority of Americans have never served in the military. Additionally, most Americans aren't "gun people". And, for my experience, the majority of military servicemembers aren't "gun people" either, and to build their confidence, are indoctrinated to believe that their M16 or M4 is the baddest killing machine on the planet.
The gun lobby takes advantage of most people's ignorance to further a political agenda. The fact is that the AR-15 isn't high powered. It isn't a machine gun. Half of the features that the anti-gun lobby villifies don't even do the things they say they do. What the AR-15 is is a tool, that in the hands of a skilled user, can be very effective for any number of lawful of unlawful purposes, just like any other tool.
Is the AR-15 a good home defense weapon (compared to a pistol or a shotgun)?
The AR-15 is a superior home defense weapon when compared to a pistol or shotgun. The AR-15 holds more ammunition in a single magazine than a pistol or shotgun. The AR-15 is easier to shoot accurately than a pistol, especially under stress. AR-15 recoils softer than any shotgun, which means you can fire multiple shots more accurately and in less time. The AR-15 is modular, which makes it easy to attach weapon lights which are critical for identifying a threat at night, and easily take optics which help with accuracy under stress or from unconventional firing positions. The 5.56x45mm or .223 Rem cartridge, which most AR-15s are chambered for is also suitable for home defense. The high velocity, lightweight projectiles give effective terminal results on bad guys, but also penetrate common house construction materials less than pistol or shotgun ammunition. Because of their high velocity, lightweight construction, bullets from AR-15s typically fragment when they hit hard objects, and the small irregular-shaped pieces don't penetrate as much as heavy, slow moving pistol bullets or buckshot pellets.
If you need proof that the AR-15 is the ideal long-arm for personal defense, look at what Law Enforcement Officers are carrying these days. AR-15's with standard capacity 30-round magazines. If a cop responding to a break-in at my house is going to be brining one, I think it's perfectly reasonable that I should be able to keep one for my own defense. Warren v. District of Columbia sets the legal precedent that the police have no duty to protect me as an individual with whom they have no special relationship