I recently (2021-04-04) heard a pastor go on and on about how Peter and John continually concerned themselves with who would be greatest in the Kingdom of Heaven. They even wanted to sit on his right and left hand. I needed to check it out.

This idea was repeated, with John and James, the next week (2021-04-11) in a sermon at another church.

First, to be correct, the following are brothers.

• Peter and Andrew
• James and John

Because the same story is in Matthew and Mark, both stories will be presented.

The "right" in the above verse is the traditional "right" but the "left" is not the traditional "left".

• The Latin word "dextrea" ≈ "right" and is the source of the English word "dexterity".
• The Latin word "sinistra" ≈ "left" and is the source of the English word "sinister".
• The modern Greek word "δεξιός" (theh-ksee-OS) ≈ "right, fortunate" (direction "northward") and is related to the Latin "dextrea".
• The modern Greek word "αριστερός" (a-ree-steh-ROS) ≈ "left, ominous".

Here are the traditional "left" and "right" from a verse earlier in Matthew.

This word for "left" appears in a number of places, including the placement of the "thieves" on either side of Jesus on the cross.

Here we may have a parallel to the parable of the sheep and goat judgment. One thief was repentant, one not.

It is not clear which thief was on which side - from the point of view of the crowd, of Jesus, from the back, etc.

It is usually accepted that Mark was writing, by and large, what Peter had told him. The primary difference in the accounts is that Mark does not mention the mother. Why might that be?

How many young men want to have their mother embarrass them in front of others? Might Peter have left this detail out?

Dr. Dobson tells the story that, when he misbehaved in school, his mother told him that if he did it again, she would come with him to school and sit with him to make sure he behaved.

Just the though of the embarrassment of having his mother there in front of the other kids motivated him to not be bad in class again.

In Matthew, the mother wants one to sit on the right and one on the left.
The terms "left" and "right" are relative to the viewer and context, so we will not be concerned about the absolute "left" and "right" directions and assume that they refer to one generic "side" .

The location of where this happens is important.

• The "left" and "right" at the physical table while Jesus walked the each is unavoidable. Someone must be on one side and someone must be on the other side and the others not on either side.
• The "left" and "right" in the "kingdom" is a different matter. We do not have full information about this "location".

The requested "left" and "right" in the "kingdom" appears to not be possible. James and John do not know for what they are asking.

It appears that no one is greater nor less than anyone else in the "kingdom".

The organizational chart of Jesus appears to have everyone at the same level in the "kingdom". No one is greater nor less than anyone else in the "kingdom". Jesus appears to emphasize this at the Last Supper, with the foot washing, etc.
The request for one to be on the "left" and one on the "right" appears to violate this arrangement. They do not appear to know exactly for what they are asking.

Jesus went on to explain how his kingdom was not a hierarchy as the kingdoms of man tended to be.

So from Matthew's account, it appears that the mother of John and James put them up to it. Or did they put their mother up to it?

These "men" were not that old as Jesus might have picked younger men that were not yet set in their ways and that would be able to do His work for many years to come.