Who should be the greatest - See on Matthew 18:1-5 (note).

But they held their peace,.... Fearing a reprimand, for their vanity and affectation of worldly grandeur:

for by the way they had disputed among themselves, who should be the greatest; that is, who should be advanced to the highest post, and have the greatest place of authority, honour, and dignity, in the temporal kingdom of the Messiah, they expected would be in a little time set up; for notwithstanding what Christ had said to them, concerning his being given up to the power of men, and concerning his death and resurrection, they still retained their former principle, to which they knew not how to reconcile his dying; and therefore chose rather to leave his meaning in suspense, and remain ignorant about it, than quit so darling a notion: and doubtless this dispute was occasioned by what Christ had said to them; who afterwards, getting by themselves, talked about it, which led on to a warm contest, about precedence in his kingdom.

But they held their peace: for by the way they had disputed among themselves, who should be the greatest.

9:34 Who should be greatest - Prime minister in his kingdom.

34. But they held their peace: for by the way they had disputed among themselves, who should be the greatest-From Mt 18:1 we should infer that the subject was introduced, not by our Lord, but by the disciples themselves, who came and asked Jesus who should be greatest. Perhaps one or two of them first referred the matter to Jesus, who put them off till they should all be assembled together at Capernaum. He had all the while "perceived the thought of their heart" (Lu 9:47); but now that they were all together "in the house," He questions them about it, and they are put to the blush, conscious of the temper towards each other which it had kindled. This raised the whole question afresh, and at this point our Evangelist takes it up. The subject was suggested by the recent announcement of the Kingdom (Mt 16:19-28), the transfiguration of their Master, and especially the preference given to three of them at that scene.

9:30-40 The time of Christ's suffering drew nigh. Had he been delivered into the hands of devils, and they had done this, it had not been so strange; but that men should thus shamefully treat the Son of man, who came to redeem and save them, is wonderful. Still observe that when Christ spake of his death, he always spake of his resurrection, which took the reproach of it from himself, and should have taken the grief of it from his disciples. Many remain ignorant because they are ashamed to inquire. Alas! that while the Saviour teaches so plainly the things which belong to his love and grace, men are so blinded that they understand not his sayings. We shall be called to account about our discourses, and to account for our disputes, especially about being greater than others. Those who are most humble and self-denying, most resemble Christ, and shall be most tenderly owned by him. This Jesus taught them by a sign; whoever shall receive one like this child, receives me. Many have been like the disciples, ready to silence men who have success in preaching to sinners repentance in Christ's name, because they follow not with them. Our Lord blamed the apostles, reminding them that he who wrought miracles in his name would not be likely to hurt his cause. If sinners are brought to repent, to believe in the Saviour, and to live sober, righteous, and godly lives, we then see that the Lord works by the preacher.