Well, microphones (at least those not powered) deliver fairly low level signals. Any RF interference could be problematic. But the RF induced voltage/current into the mike cable would have the same polarity on both conductors. In other words the received radio signal is in-phase on both wires, or is in common-mode. If the mike is a balanced emitter of signal into a differential amp on the receiving end (or the primary of a transformer), then that differential amp input is only seeing the difference in voltage between the two conductors. The common-mode (in the same polarity on both conductors) RF signal is rejected by the differential input of the amp. (Common-mode rejection)
So, mikes use blanced signal trasmition for is common-mode rejection capability to rid signal of induced noise on long cable runs. (Not only RF from radio, but RF from flourescent lights and refridgerator motors as well.)
But with headphones, the high signal levels and low output impedance of the amp make developing an RF signal on the wire much less of a problem. Balanced is use on headphones so that you can rid yourself of cross-talk from the common ground with normal headphone wiring. Also because you have two amps slewing in opposite directions, you effectively double the slew rate of your electronics. Unfortunately, it also doubles the output impedance of the amp, so it lowers the damping factor. Lastly, it tends to cancel out some of the even order harmonic distortion products of the amp. To me that's why it's kind of stupid to build tube balanced amps that have amp stages for both + and - channels. But we're getting way off topic now.