In a gunfight, most shots fired miss, so you want extra tries.
I don't own an AR-15 myself. My interests lie elsewhere. I have fired or examined a representative sampling of AR-15 and M-16 weapons, though. Every citizen should have a working knowledge of the service rifle, even if he prefers something else.
I will, however, argue that an AR-15 is entirely a suitable weapon for defense of home and hearth, thus just the sort of thing the Second Amendment has in its view to protect. For many families' purposes it is an ideal choice.
The wife and kids can shoot it if they have to
The type is inherently easy to shoot. Its good ergonomics, straight-line stock and light recoil make it easy to manage, even for women and teens. Here is a story where a teen used his dad's AR-15 to defended himself and his sister.
It is quite accurate
More so is better than less so, in a defensive firearm. The AR-15 is more accurate than most comparable types. That also helps to sell it as a target shooting firearm and for varmint hunting and farm pest control. It's a good multi-purpose use of your shooting money--it's not just for home defense. You will shoot better with a gun you shoot a lot, so it's a good thing if your home defense rifle is also your range gun and your varmint gun.
It's safer than many other guns to shoot indoors or near houses
Its small speedy bullet poses less over-penetration risk in common building materials than typical defensive pistol and shotgun projectiles. Thus it is safer to use in and around people's dwellings. That is among the reasons why many police departments have gone to AR-15's to arm their officers.
It holds plenty of bullets
That's something the anti-gun folks don't like, but in a gunfight, most shots fired miss, so you want extras. That's the real reason for big magazines on police, military and home defense rifles. Even crack shots sometimes falter in their aim when their knees are knocking, their adrenaline is pumping and chunks of lead are sailing around. Thus it is entirely appropriate for your rifle to hold more than ten shots if someone is shooting at you. Add the possibility of multiple criminal assailants and a thirty round magazine is none too big. And, anyway, the bad guys aren't paying attention to any magazine ban.