The purpose of ministering deliverance
Guess what? This ministry isn't about demons! That's right! It's about guiding and helping our brothers and sisters come into the victory that Christ died to give them! The purpose of ministering deliverance is to set free those who are in bondage. As Jesus was sent fourth to preach deliverance to the captives (Luke 4:18, "The Spirit of the Lord is upon me, because he hath anointed me to... preach deliverance to the captives..."), so we are also sent out (John 20:21, "Then said Jesus to them... as my Father hath sent me, even so send I you.") to do the works He did (John 14:12, "He that believeth on me, the works that I do shall he do also..."), and this includes casting out of devils (Matthew 10:8).
The ministry of deliverance is about bringing spiritual victory and freedom to those who are in bondage. It doesn't matter what you call it (demonized, possessed, oppressed, etc.), if they are in demonic bondage, whether they need to tear down a stronghold, break up a legal ground, cast a demon out, or all three... it's still deliverance, because it's setting the captives free. Casting out demons, is just part of the overall ministry of deliverance.