It's hard to top the Haydock commentary for this so I'll just cite it and link to it (though I did add the emphasis):
Ver. 1. Who, thinkest thou? This altercation for superiority among the
apostles, whilst they were upon their road to Judea, might have arisen
from another cause besides the precedence given by Jesus Christ to
Peter above, as St. Chrysostom (hom. lix. in Mat.) affirms. A report
prevailed among the disciples, that Christ would soon die; and they
wished to know who would be the first, when he was gone. (Jansenius)
--- Or expecting that by his future resurrection he would enter into full possession of his temporal kingdom, they wished to learn which of
them should be the greater in this new and glorious state. Calmet
supposes that Peter was not with them, but that he had gone before
with his Master to Capharnaum. (Calmet)
Ver. 2. And Jesus calling ... a little child. In St. Mark (ix. 32.) we
find that Jesus did this in the house, when they were arrived at
Capharnaum.
Ver. 3. You shall not enter, &c. i.e. you shall have no place in my
kingdom of glory, in heaven, where none shall find admittance but they
that are truly humble. (Witham) --- Our Lord in this and the next
chapter teaches us, 1st, To sit down in the lowest place; 2nd, to bear
patiently with our neighbor; 3rd, not to scandalize a weak brother;
4th, mildly to correct him when faulty; and 5thly, to forgive him when
repentant.
Ver. 4. Greater in the kingdom of heaven, because more conformable to
me here on earth. Humble souls, who are little in their own eyes, are
so dear and closely united to the Almighty, that Christ declares them
to be the most acceptable, the first in merit, not highest in
authority or dignity either in church or state, as some idle fanatics
pretend. (Jansenius) --- The kingdom of heaven is not the reward of
ambition, but the boon of simplicity and humility.
Link: http://haydock1859.tripod.com/id36.html