Air combat, unfortunately, is one of the most obscure topics in the Civilopedia - that is, everything is explained but severely lacking in details.
In particular, I've noticed that when using the air strike mission, sometimes the attacked target will shoot back and sometimes it won't. I'm talking about regular shooting back, not the special attacks of anti-air units (such as destroyers) or interceptions by defending aircraft.
When I attack a unit or a city it will sometimes shoot back and sometimes not. Does anyone know the rules behind this? It doesn't seem to be entirely random, but I could not find any truly consistent behavior. I'm going to post an answer with what I know so far, but I would really like to see something more complete.