Does the Bible address the topic of the origin of demons? Are they spirits of the dead or spirits of the fallen angels? Alexander Campbell delivered a very learned lecture in Nashville, Tennessee on March 10, 1841, in which he, in rather persuasive fashion, argued the case that the demons of the ancient world were the spirits of the dead.
Also 1 Timothy 4:1 states that people in later times will be misled by the teachings of demons. So does that imply we are still witnessing demonic activity even today?
The reason that there are debates about demons, even among conservative scholars, is that the Bible does not provide much specific information about their origin and even how they function in the world today. What seems to be clear from passages such as the one you quote from 1 Timothy 4:1 is that demons still exist and they are still attacking both believers and non-believers.
We must do at least some speculating, so let me speculate. I believe that demons are angelic beings who rebelled against God and lost their place with him. I believe this because this almost certainly appears to be true of Satan himself. Satan clearly pre-existed Adam and Eve, as is seen from Genesis 3. Everything that God created is good (Genesis 1:31). Therefore, I conclude that Satan himself was created good, but with some sort of “free will.” I believe, therefore, that he rebelled and was cast out of his place in heaven, coming down to attack God’s greatest creation–human beings. Revelation 12:1-9.
To apply this explanation to demons is somewhat problematic, as I have no equivalent passage about demons to support my thought about how they were created and how they were turned toward evil. In any case, I do not believe that they were created evil, so they must have turned against God after their creation. Could they be former humans–“spirits of the dead” as Alexander Campbell believed? I cannot disprove this idea, but it is not my belief on the topic. From my perspective, the dead are not mere “spirits”. I believe that when we die we will have a different but physical body, so we could not become “spirits.” Nevertheless, I believe that this is not an essential or even an important doctrine. What is important is that we understand that there are spiritual forces of evil in the heavenly realms (Ephesians 6:10-12) who oppose us, but also that God is in control and that demons and other evil powers cannot overcome us if we trust in God.
So, like I said, I believe that demons are “fallen angels” not spirits of the dead, but this is an interesting but unessential biblical teaching. What is essential is that we realize that Satan is real and we should be aware of his schemes (2 Cor 2:11) but not fearful, as for us Christians, God is in control.