If it is not to much of an epic typing session: How does this miss identification occur, it baffles me.
On light twins, it is “dead foot, dead engine” (which rudder is not needed to maintain direction of flight). On airliners, it begins with maintaining direction, WITHOUT concern with which engine failed, until above a critical altitude, where a discipled two-pilot confirmation of which engine failed (engine instruments) process correctly identifies which engine has failed to prevent this very occurrence.
So, the confusion comes when “little airplane” pilots fly big airplanes, and forget big airplane training and disciple, and instead doing stupid things.
How do pilots do the “wrong” thing and crash, in a few short sentences? Well, there are technical answers, and there are human factors. On the technical side the short answer is, it’s not always easy. There have been accidents where an engine has failed and the pilot NEVER realized he’d had an engine quit. Sometimes an engine only partially fails. It can be tough to tell which engine is rough?
On the human side, things get even more complex. Panic sets in. Pilots get “task saturated” and just can’t process what they are looking at. Sometimes in haste they just grab the wrong lever.
The bottom line is, it takes a lot of training and then a lot of practice after the initial training to be ready when the time comes.