There is no question that bird shot can be deadly at close range.
But advocates of the shotgun for home defense often make two claims that don't stand up to testing.
The first is that "you don't have to aim or anything, the room will be filled with a cloud of shot that will kill anybody in there." Since the average spread of a shot charge is about 1" per yard, the shot spread across an average room will be about 3-4 inches, hardly a "cloud of shot" that eliminates any need for aiming or even pointing the right direction.
The second claim is that "birdshot will not penetrate dry wall or anything else so your loved ones will be safe." Not true. Any shot load with the power to kill or seriously wound an intruder will have enough power to harm innocent people, even behind dry wall.
That is very true. You still have to aim a shotgun. You cannot just point it in a general direction, and hope to be successful.
A shotgun would be most useful in protecting your home in case of a riot or other type of breakdown in civil order as took place during Katrina, or the LA riots.
But against an intruder inside your home, a good handgun is still your best option.