Here is an excellent example of an article knocking shotguns, that is wholly inaccurate. But the article has quite a few good points: People like shotguns because they were very popular for a very long time as the "one gun to have".
http://dailycaller.com/2015/08/21/home-defense-ar-vs-shotgun/
The article also has a VERY bad suggestion with shotguns: using bird shot.
My primary reason for NOT using a shotgun is the recoil. Beyond that, the myths are just that: "Can't Miss", the "click-clack" will make a robber run away, they don't penetrate walls, etc.
When the SHTF around here in August/September, the AR was with me. We had looters in our neighborhood and in our business park. If you "THINK" you need a gun, bring a rifle and friends with rifles.