When you read the passage where Jesus tells us that it is unfit to cast the children’s bread before dogs, has it ever occurred to you that Jesus actually refused to cast a demon out of people who were not in covenant with God? Of course, once He saw her faith in Him, that changed everything. I just think that is really interesting that Jesus would refuse to deal with a demon in somebody, just because they were not in covenant with God. He said that it was unfit to take the children’s bread (deliverance) and give it to dogs (those outside covenant with God). It was UNFIT, NOT RIGHT, NOT MADE FOR… get the point?
But besides that, why would we want to cast demons out of non-believers when the cards are clearly stacked against such a practice? First of all, the demons have not been disarmed, because the person’s sins have not been forgiven. Secondly, why do you think Jesus warned against casting demons out of people if they were going to come back with 7 even more evil spirits? Do we really think it’s wise to run a non-believer through deliverance, given that kind of a warning?
And finally, do you honestly know of somebody who claims to cast demons out of non-believers only, and has a lot of genuine success and fruit from it in their ministry? I don’t know of a single minister who does such a thing, and I don’t think you do either.