Maybe your problem is pigheadedness and not ignorance after all. The Pharisees questioned Jesus about His having cast out demons and suggested that He was acting under Beelzebub's, not God's authority (just like you did). Jesus provided the logical argument that that was ridiculous (just like I did)
Satan uses whatever means necessary to keep the lost from finding the truth. Satan co-operates with false religions, which he himself has founded to deceive men. He heals people without their faith in Jesus and His finished work on the Cross. He gives signs and wonders and miracles to keep the unsaved believing that it is God who is doing these things. Such people naturally think they are in the TRUE RELIGION. Satan has won their souls with his shows of power. Demons can go out and come back into a person of their own accord.(Mt. 12:43-45). Satan gives power to his duped followers, thinking they are doing the works of their Father, God. When they are doing the WORKS of their real father, satan. Exorcisms, prayers to the dead, apparitions of Mary, wafers and wine turning into the body and blood of Christ, etc. The "signs and wonders" meant to deceive. And it's working very well.