Why is it so easy to tell the difference between live and recorded music?

When I played "Jazz Wolf" CD, even on a very low-end mini system, my dog would Always join all those other wolfies "out there"! It was fun!!
Better hearing or not, personal involvement must have played a role. Music or sounds coming from TV never fooled him

I was fooled by my stereo more than once: when listening to Roger Water's "Amused to Death" I always thought that its a neighbors dog barking outside. It was recorded thru some Q-Sound effects, but as mentioned already by @gs5556, my expectations fooled me. The effect is lost thru the headphones. 

Aside from the fact is the listener usually knows beforehand if what they are listening to is live or not, it’s not always so easy assuming a good setup and good recording to go with it. There are often many clues in a studio recording that will give it away as not being live but not always.

Dynamic range certainly plays a huge role.

I also notice the ability of many a system to start and stop fails to mirror reality, even as some claim the superiority of their means of implementation.

But for me, I'm MOST bothered by the incorrect tone / timbre of most high-end audio systems, even when they possess notable dynamic range or speed.  There's simply an unnatural sonic signature to most high-end audio components / systems I encounter.  I cannot get past that

Some of Frank Zappa's stuff is very hard to tell if it is live or not. Mostly very well done.

Frank Zappa’s entire catalogue or most of it has one outstanding characteristic. Dynamic range. The Official Dynamic Range Database. Check it out.