One of the enduring frustrations of the church is the continued existence of the self-righteous hypocrite.  In every age the church has had such people, often in high position, and the question comes up,  "How can we deal with such people?"
One of the ways Christ used is shown here.  There is no sense here of fire and wrath, but rather of sweet reasonableness.  This tends to keep them listening, rather than putting them on their dignity.  The temptation is to poke holes in pomposity, but our Lord never does that--his care is for the lost, and he will do what it takes to bring them to salvation.
Notice, please, that he answers their thoughts.  How often the hypocrite thinks he has everyone fooled, and how often he is wrong!  Jesus does not tell them what they are thinking;  he simply responds to it.  This gets him a better hearing now;  it most likely caused them some reflection later.   After all, it's like the man could read their minds!
Most important, he appeals to what they know, in a common sense way.  He points out to them that there are Jewish exorcists who do the same thing--calling upon the name of God.  If they do it that way, what is so unlikely about Jesus doing the same?  Indeed, if Satan is casting out Satan, he's finished--and the kingdom of God is here.  But if God is casting out Satan, then Satan is finished--and the kingdom of God is here.  The logic points only to one thing:  the kingdom of God is here.
Note, interestingly, that he does not use the Scriptures here.  In his gentleness he is avoiding a debate about words and meanings.  This is not something to be tightly reasoned from Leviticus, but rather to be seen with the eyes and heard with the ears.  The evidence is at hand.

It is a curious thing.  The man who is brought before Jesus is both blind and deaf.  In the technology of that time, he would be unable to be saved--for he could neither hear nor read the good news.  By his demon possession he would be kept from the kingdom.  But Christ throws this demon out, for it is God's will that all should be saved. 
The hypocrite, too, is blind and deaf.  But by the gentle prodding of God's people, their continued love and refusal to accept hypocrisy, the eyes and ears of the hypocrite can be opened.  I know of at least one such, and I am eternally grateful.