Turn Down Your Volume!
You wouldn't play around with speaker cables while your power amp is on because you know the leads might short together and blow up the amp! Well, a headphone amp is a miniature power amplifier, so when you plug and unplug headphones the contacts do short to ground momentarily, and you can blow up a headphone amp plugging in headphones. We could design in protection circuits, but we don't because they sound notoriously bad. So PLEASE, turn off, or at least turn fully down, your headphone amplifier before plugging in or unplugging your headphones.
Incidentally, there are other reasons to turn down the volume on your headphones, even while listening. Learn about avoiding tinnitus.