The Brief: Dragging means to roast or insult someone.

DEEP DIVE
The term drag or dragging has multiple meanings. This one is often used online. A self-drag is when you intentionally humiliate yourself, usually for laughs. Finsta posts often include self-drags.
cher dragging dr. pepper pic.twitter.com/tqchWj63zv
— cher doing things (@cherdoingthings) August 15, 2018