The problem with Run DMC was the same as with every rap band/artist, they just had to sing about how everyone else sucked and how good they were. 
That is what diss records do...that was the nature of the game back then, and still is...rap is about bragging....one can use rap like Common or Talib, or Mos Def, or Arrested Development, or Bahamadia...but ultimately it was about having a fun time and bragging about how good you are..a "top that" mentality...which means the better, more imaginative rapper was better..
