See (Luke 22:27).   In (Luke 6:40) the contrast is between the pupil and the teacher, but the lesson is the same, and in (Mat 10:24) Jesus uses both pupil and slave to illustrate His point. Obviously, He repeated this comparison often. Why?

Luke 22:27  For who is greater, the one who is at the table or the one who serves? Is it not the one who is at the table? But I am among you as one who serves.

Luke 6:40  A student is not above his teacher, but everyone who is fully trained will be like his teacher.

Matthew 10:24  “A student is not above his teacher, nor a servant above his master.

R. Meir says, ” who is greatest, he that keeps, or he that is kept? from what is written in (Psalms 91:11), he that is kept, is greater than he that keeps: says R. Judah, which is greatest, he that carries, or he that is carried? from what is written in (Psalms 91:12), he that is carried, is greater than he that carries: says R. Simeon, from what is written, in (Isa 6:8),  “he that sends, is greater than he that is sent”.”   (Bereshit Rabba, fol. 68. 1.)

Psalms 91:11  For he will command his angels concerning you to guard you in all your ways;

Psalms 91:12  they will lift you up in their hands, so that you will not strike your foot against a stone.

Isaiah 6:8  Then I heard the voice of the Lord saying, “Whom shall I send? And who will go for us?” And I said, “Here am I. Send me!”

In the Midrash “it is proverbially said, that while he that is sent stands on the same footing as he who sent him, yet he must expect less honour.” (Edersheim)

Jesus is telling them that they should not think too highly of themselves, but realize their relation to the One Who has just given them an example.

We owe everything we are and everything we have to Jesus. He is our life and our enabler.