"But light cannot dwell with darkness!"
This is perhaps the most common argument raised against the idea of a believer having a demon. This assumption is mostly based upon 2 Corinthians 6:14, which is actually lecturing the saints about believers marrying unbelievers:
"Be ye not unequally yoked together with unbelievers: for what fellowship hath righteousness with unrighteousness? and what communion hath light with darkness?"
It is important to point out that it is not telling us that a believer cannot marry a non-believer. It is merely pointing out that there would be no communion (partnership) between the two. How can they share the same spiritual goals if one is spiritually dead and the other alive? It's impossible. But does that mean a non-believer cannot marry a believer? Of course not!
Obviously the Holy Spirit (light) will not partner with the demonic spirits (darkness) in a person either, but that doesn't mean the two cannot coexist. Just as a believer (who is of the light) is quite capable of marrying a non-believer (who is in darkness).
Man is composed of a body, a soul (mind) and a spirit.
1 Thessalonians 5:23, "And the very God of peace sanctify you wholly; and I pray God your whole spirit and soul and body be preserved blameless unto the coming of our Lord Jesus Christ."
Our spirits are reborn instantly the moment we call upon Jesus to be our Lord and Savior. 2 Corinthians 5:17 makes it clear that all who are in Christ are new creations.
"Therefore if any man be in Christ, he is a new creature: old things are passed away; behold, all things are become new."
When we accept Jesus, our spirits are united with the Holy Spirit. The Holy Spirit dwells within our spirits. But there's another part of us that has not been instantly and wholly changed the moment we became children of God.
Your soul, which is your mind, was not instantly changed the moment you accepted Jesus. This is where the old fleshly nature can still be lingering in a believer's life. This is the part of us that Romans 12:2 is referring to as we are told to be renewed in our minds:
"And be not conformed to this world: but be ye transformed by the renewing of your mind, that ye may prove what is that good, and acceptable, and perfect, will of God."
This is why new converts often carry over so much darkness in their lives even after accepting Christ. When is the last time you met a believer who can confidently claim that they've never sinned since the moment he has accepted Christ? Unless you happen to catch them on their way back to their seats from an alter call, I doubt you'll find many.
We are given a new nature when we are born again, our old sinful nature is circumcised (cut) from us, and we are given a new nature in Christ Jesus. But in Colossians 3:10, we are also told to put on this man by growing in the knowledge of Him that created us:
"And have put on the new man, which is renewed in knowledge after the image of him that created him."
The more we spend time and fellowship with the Lord and in His Word, the more we put on the new nature in Christ Jesus, and our minds are transformed. As Ephesians 5:26 tells us, we are cleansed by the washing of the Word:
Ephesians 5:26-27, "That he might sanctify and cleanse it with the washing of water by the word, That he might present it to himself a glorious church, not having spot, or wrinkle, or any such thing; but that it should be holy and without blemish."
Apparently, if light could not dwell with darkness, then it would be impossible for Paul to have the Holy Spirit or to even be a believer for that matter, at least according to Romans 7:17-18:
"Now then it is no more I that do it, but sin that dwelleth in me. For I know that in me (that is, in my flesh,) dwelleth no good thing: for to will is present with me; but how to perform that which is good I find not."
So if light cannot dwell with darkness, how would it be possible for Paul to have the Holy Spirit dwelling within Him, and still have darkness dwelling within him as well? Apparently, the two can coexist.
In Jeremiah 23:24, God tells us that the Holy Spirit covers the whole earth:
"Can any hide himself in secret places that I shall not see him? saith the LORD. Do not I fill heaven and earth? saith the LORD."
If the Holy Spirit covers the earth, and darkness could not dwell in the light, then that would mean demons would be incapable of roaming this earth.
In Job 1:12, we are told that Satan himself, the king of darkness, has been known to approach even the presence of the Almighty God:
"...So Satan went forth from the presence of the LORD."
Demons are known to operate in both the soul and the body.
There is no Biblical evidence that I am aware of where demons are known to specifically operate within a man's spirit. Every time we see a demonic spirit at work in the life of a person, it is either through the soul (mind) or the physical body. In Matthew 17:15,18, we find an example where a young boy was mentally ill because of a demonic spirit:
"Lord, have mercy on my son: for he is lunatic, and sore vexed: for ofttimes he falleth into the fire, and oft into the water. And Jesus rebuked the devil; and he departed out of him: and the child was cured from that very hour."
The term lunatic here in the NT Greek translates to the word seleniazomai, which means moonstruck or crazy. To be moonstruck literally means mentally unbalanced, or mentally ill. Clearly the boy was affected mentally by this evil spirit.
People are also known to be physically affected by demonic spirits. In Luke 13:11, we are shown of a perfectly sane woman who was physically bound by a spirit of infirmity:
"And, behold, there was a woman which had a spirit of infirmity eighteen years, and was bowed together, and could in no wise lift up herself."
It is not uncommon for people to be tormented and harassed with fear and other mental torment, such as the case 1 Samuel 16:14, where King Saul received an evil spirit:
"But the Spirit of the LORD departed from Saul, and an evil spirit from the LORD troubled him."
When we trace the word troubled here back to the OT Hebrew, it gives us the word baath, which means to terrify, trouble or overwhelm a person. It is not uncommon for people to be mentally harassed by evil spirits in this manner.