Telephone Tag Meaning
(idiomatic) A situation in which a person unsuccessfully attempts to contact another person by telephone and leaves a message instead, and in which the second person then unsuccessfully attempts to return the initial call and leaves a message for the first person, and so on as if the two are playing a game of tag in which the most recent person to have been left with a message is now designated as "it" (i.e. as the player now obliged to chase the other and to attempt anew to make contact).
Example: 1998 August 17, Christine Gorman, "E-Mail Your Doctor," Time:
Playing telephone tag with your doctor is one of the most commonâ€”and frustratingâ€”rituals of modern medicine. You phone...can't get past the receptionist...leave a message. Your doctor calls back while you're in a meeting...leaves a message. The amount of time wasted on both sides turns everybody sour.