Rather, the word demon-possessed is translated from daimonízomai which means to be demonised. The more accurate term would be demonised, not demon-possessed. Demonised means to be under the control of a demonic spirit.
The Christian does struggle with sin and is tempted by satan and his demons who try to distract, tempt or oppress him. For we wrestle not against flesh and blood, but against principalities, against powers, against the rulers of the darkness of this world, against spiritual wickedness in high places (Ephesians 6:12). Demons are active in this world and attempt to attack Christians the most because they do not want the Church to reach more souls and expose evil spirits. They do not want to be understood by the people who should and have the ability to - the Christians.