Keep diligent records of the incidents and, perhaps most importantly, your husband's reactions. It shouldn't take long to see a pattern. You may also want to document information from other sources, such as grandparents, playmates' parents or schoolteachers. Record the adult's version and your stepchild's version. Again, you should see a pattern.
Verbal arguments tend to be highly emotional and poorly remembered.
Again, your husband may not believe you, but you'll have a written record, and that's hard to argue with. Save yourself the trouble of explaining or justifying anything. Just show him the documentation. Then the decisions are up to him. Unfortunately, some children feel that their purpose in life is to break up the marriages of their parents.