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

Hahaha!!!

She IS fast...

Mostly because your brain is telling you there's no way it could be live music when the eyes transmit to it an image of speakers. Place musicians on a stage pretending to play while a pair of speakers behind them actually play, then it gets more difficult to tell the difference.

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.