Many millipedes do this when handled, it may be because many species seem to enjoy eating keratin, which is what our skin, hair, and nails are made of. Chitin, which makes up a millipedes exoskeleton, is also similar to keratin from what I hear (I am not 100% sure however), so it may be that they mistake our skin for chitin, which they eat on occasion in preparation for their next molt, causing this behavior.
People with a low pain tolerance (like myself) may feel the chewing as painful pinches or uncomfortable rasping, and I believe larger species may chew enough to cause a large pinching feeling even for those with a high pain tolerance. What kind(s) of millipede do you have?
Hope this helps,
Arthroverts