I think... it began with the producers wanting them to fight and insult each other, for the sake of rivalry and drama.
But even though that was sort of manufactured (or fake) in the beginning, their insults in public really do irritate each other.
It doesn't really matter if Cathy does a fat joke because "it's her job" to create drama; it's still going to make Abby angry.
And it doesn't really matter if Abby is saying that Cathy has no talent or ability, as part of her job; it's still going to annoy Cathy, especially when fans repeat those ideas.
The end result is that they genuinely do hate each other now.
Now that's just my guess as to what's evolved, and I could be wrong...