Jesus defines a demon as an ‘unclean spirit’ and personifies it to teach a lesson about apostasy.
Matthew 12:43 When the unclean spirit is gone out of a man, he walketh through dry places, seeking rest, and findeth none.
Spirit is the way that we think; an unclean spirit therefore denotes a deranged mind.
When the unclean spirit is expelled, the man is said to be ‘in his right mind’.
Mark 5:15 Then they came to Jesus, and saw the one who had been demon-possessed and had the legion, sitting and clothed and in his right mind. And they were afraid.
Describing mental illness as ‘demon possession’ is not a problem if we understand what an unclean spirit represents.
The basic understanding of the truth is that there is no supernatural power but that of God. Ergo there can be no such thing as a ‘demon’. A Jew who understood the scriptures would not be confused. The existence of demons springs from a belief in pagan gods.
I would speculate that Jesus does not specifically state that demons do not exist for the same reason that he spoke in parables. His hearers need to make an effort to understand him based on scripture.
I hope this helps