The popularity of the AR-15 is related to the popularity of the M16, but the "pretend you're a soldier" aspect isn't the main reason. A more complete explanation includes:

- Lots of manufacturers

- Reliable action (depending on manufacturer)

- 5.56mm NATO and/or .223 Remington ammo is (or, before late 2012, was) relatively cheap

- Light recoil

- Tons of accessories available

- Relatively accurate

- Fun to shoot

And also, among gun guys, there's at least a little bit of the feeling that by owning one, you're giving the middle finger to people who want to ban them.