Luke 11:14-28 (ESV)
Now he was casting out a demon that was mute. When the demon had gone out, the mute man spoke, and the people marveled.  [15] But some of them said, “He casts out demons by Beelzebul, the prince of demons,”  [16] while others, to test him, kept seeking from him a sign from heaven.  [17] But he, knowing their thoughts, said to them, “Every kingdom divided against itself is laid waste, and a divided household falls.  [18] And if Satan also is divided against himself, how will his kingdom stand? For you say that I cast out demons by Beelzebul.  [19] And if I cast out demons by Beelzebul, by whom do your sons cast them out? Therefore they will be your judges.  [20] But if it is by the finger of God that I cast out demons, then the kingdom of God has come upon you.  [21] When a strong man, fully armed, guards his own palace, his goods are safe;  [22] but when one stronger than he attacks him and overcomes him, he takes away his armor in which he trusted and divides his spoil.  [23] Whoever is not with me is against me, and whoever does not gather with me scatters
A demon has made a man unable to speak. In some Christian circles, some of which are very active in the area where our church does its work and some of which teach their strange doctrines to people in our church, it is taught that all sickness is due to some form of demonic activity. This text is one of  the ones that is used to support the claim.
This text is neither teaching that all muteness is due to demons or that all sickness is due to demons. The New Testament writers knew the difference between sickness and demonic activity
Luke 4:40-41 – Now when the sun was setting, all those who had any who were sick with various diseases brought them to him, and he laid his hands on every one of them and healed them.  [41] And demons also came out of many, crying, “You are the Son of God!” But he rebuked them and would not allow them to speak, because they knew that he was the Christ.
Matthew 4:24 – So his fame spread throughout all Syria, and they brought him all the sick, those afflicted with various diseases and pains, those oppressed by demons, epileptics, and paralytics, and he healed them.
Note it well. Both Matthew and Luke distinguish between those who are sick, epileptic, demon possessed and paralysed.
There are Christians of various types who attribute all sickness to demonic activity. Most of the time it seems that any time you disagree with them they accuse you of having a demon. And it seems quite often that God sends them to tell you just how demon affected you may be and just what the solution is. The New Testament will not tolerate such nonsense. The authors of the NT spoke of illness, insanity, demon possession, epilepsy as causes for various disorders. We must not jump at the conclusion that a person’s illness, seizures or unusual behaviour are the work of demons. They may be the work of chemicals, biology, environmental matters, unhealthy living, mental disease or, in very rare situations – demons. Demonic activity is extremely rare in this part of the world and we should be thankful.
There are demons in the world and they are very active. But the child of God is not a slave to them. This is what Jesus is getting at in the verses following the ones in Luke quoted above.
Luke 11:24-26 – “When the unclean spirit has gone out of a person, it passes through waterless places seeking rest, and finding none it says, ‘I will return to my house from which I came.’  [25] And when it comes, it finds the house swept and put in order.  [26] Then it goes and brings seven other spirits more evil than itself, and they enter and dwell there. And the last state of that person is worse than the first.” 
In other words, when Jesus gets us out from under the influence of our sin and demonic activity, He does not leave us empty. The Holy Spirit comes and dwells in us (Ephesians 1:12-14). An evil spirit cannot take up residence in a true child of God. The room is occupied.
Quite often, those who hold to seeing demons as the cause of all our sickness also believe that sin is the result of demon activity in a person as well. Scripture won’t let us get away with that either. We sin because of our own sinful desires. When I sin there may be various outside forces enticing me to do so but the Scriptures are clear that God has given us everything we need for life and godliness (II Peter 1:3). I cannot explain my sin, or the sin of any other believer, as the work of a demon on some hapless, helpless victim who had no choice. Christians are indwelt by the Holy Spirit (Romans 8:26), have the completed Word of God at their fingertips (II Timothy 3:17), are part of a fellowship of God’s people (Hebrews 3:12-13), are able to cry out to God for help  (Ephesians 6:18). It is the lack of the use of these things in us that explains our sinfulness. Sin is the result of our own sinful hearts.
Finally there are those sceptics  who read a text like Luke 11 and conclude that the Bible is just an old book of superstitions that attribute blindness and other ailments to evil demons when we know today that they are the result of a myriad of other things. But as we have noted, the New Testament authors recognized all kinds of reasons for all kinds of ailments. The fact that demons are included as one cause among hardly means that the Bible sees demons as the only cause of the problems. The man in Luke 11 was made mute by a demon. Others were sick for other reasons and that is what the Bible notes. We make no apologies for acknowledging the truth of the spiritual realm that acts beyond what we can put in a test tube.
And above all of these things is the great truth that this man encountered a compassionate, powerful Saviour. He uses His power for our good, and that is the greatest truth of all in this text.