Board Thread:Fanon Canon/@comment-2089817-20180513110249/@comment-3403804-20180520073829

Basically what Z said, they want independence, and I assume that the Gotei 13 want to prevent that and subsume the Coven back into its fold, similarly it wants to prevent a new third party group from forming outside of their control, because it might endanger the super fragile human world. This means that it makes more sense for the Gotei to have the attacking role early, while the Coven draws influence from all manner of foolish humans, and makes deals with otherwordly entities and spiritual creatures to assist them in that venture, such as Arrancars and others.

Now whether or not the Coven simply wants to establish its own state, which would probably be in Hueco Mundo since it is the realm where kido specialists are at their definitive strongest, the Gotei 13 will have reason to oppose their goals. Ultimately, I think the Coven wants to reset Soul Society to what it used to be, rather than the overwhelming oligarchy that it is today, but their methods are quite extreme and not all amongst their number are neccessarily that motivated by being forces of change as much as they're simply people looking for revenge. Such as my own Megumi and Yuuna.