This semester I have been asked to help evaluate some of our student's preaching. This has been a helpful exercise for me and I hope also for the students. Yesterday, a student was preaching on Luke 7:1-10, the healing of a centurion's servant. There was much to commend about the message but the student seemed to struggle with the central idea of the text (i.e., the CIT or message). In my remarks, I suggested that one should remember that in narrative, dialogue/monologue when present, tends to do the heavy lifting an therefore one should start there in seeking to find the main subject. Indeed, when dialogue/monologue is present, the main function of the rest of the narrative is often to frame it. In 7:1-10, most would identify three monologues.
The Jewish elders tell Jesus: “He is worthy to have you do this for him, for he loves our nation, and he is the one who built us our synagogue” (vv. 4-5).
The centurion's friends tell Jesus: “Lord, do not trouble yourself, for I am not worthy to have you come under my roof. Therefore I did not presume to come to you. But say the word, and let my servant be healed. For
I too am a man set under authority, with soldiers under me: and I say
to one, ‘Go,’ and he goes; and to another, ‘Come,’ and he comes; and to
my servant, ‘Do this,’ and he does it” (vv. 6-8).
And then Jesus himself states: “I tell you, not even in Israel have I found such faith” (v. 9).
Now if one looks at the words of the elders (vv. 4-5), one might think that "piety" might be the main subject of the passage. Piety might also find some affirmation in the words of the centurion's friends (vv. 6-8). But Jesus words in v. 9 do no highlight the centurion's piety.
One might also look at the longest bit of monologue (vv. 6-8) and guess that perhaps authority or humility are the main subject. Concerning the former, one could find some implicit support in that the Jewish elders are authoritative figures and the fact that another authoritative figure, a centurion is involved, and that ultimately Jesus has the authority to heal. But again, Jesus words in v. 9 do not seem to directly address the issue of authority or humility. Indeed, Jesus' authority to heal is implicit: "And when those who had been sent returned to the house, they found the servant well" (v. 10).
As you might have guessed by now, Jesus'  words hold the key to the main subject, namely faith. The Jewish elders appeal is based on merit and not faith. Note the subtle rebuke in v. 9: "not even in Israel." The centurion's friends do talk about authority but as Jesus notes, the words ooze with faith. Jesus does not "marvel" at the centurion's piety, authority, or humility, but his faith.
So if this is correct, the main subject of 7:1-10 is faith. From there one might decide whether authority, humility, etc., might be complements and therefore still included in one's CIT.
 In examining monologues and dialogues one should also take into consideration "who" is speaking. Some words are more significant because some characters are more significant. This is generally true when you have round versus flat characters. In the Gospels, it is obvious that Jesus and his words have pride of place and therefore, his words trump the words of others. It is also word noting that Jesus' words are the most direct words in this pericope. The Jewish elders convey the request of the centurion and the centurion's friends convey the words of the centurion. Indeed, the centurion never addresses Jesus directly. Only Jesus speaks for himself.