From the very beginning Ashley and McRose have clashed with personality, fists, verbal taunts, you name it. The two have always been strong woman, which served as the exact fact as to why they bickered so often. Though at first it was more playful, no ill intentions behind their actions. Strong personalities were meant to bump now and then, after all.
This initial disagreement eventually further blossomed into an outright hate for one another, the sole cause for this being each of their bloodlines. You see, Ashley was a women who had never been particularly well off and was much distrusting of royal blood, and Levy's lineage didn't do anything short of fuel that fire.
Of course, as much as Levy tried to prove that she was against Faust's rule, all of that was shot to shit one day that Fairy Tail was almost caught due to a slip up from Levy's side. That night Levy had come across her brother, and nearly got Fairy Tail caught due to her need to see him. This same meeting almost lead to her death as her brother dug a blade into her, hilt touching hot skin. It was Ashley who saved her that night, wrapping her whip around the man's throat and pulling him off Levy, nearly killing him for hurting her guild member. He was trash to Ashley, but Levy still saw that man as family and a best friend, so she flung herself at Ashley until the woman loosened the hold on her brother.
The man was left there on the floor, passed out, but still very much alive. And though he didn't die that night, hurting her brother made Levy despise the woman with every portion of her being. This made her associate the woman with barbarians and amazons, who were much too brutal in nature to hold common sense.