To understand why the disciples acted as they did, the society of their time must be better understood.
Observant scholars of the Bible will notice cultural cues embedded in its stories. The society of that day was more typical of an Eastern collectivist mindset than a Western individualist mindset. One's identity in an Eastern culture is highly dependent on one's relationships with others in the group.
For example, in the Eastern society of Asia today, one fairly common question that may be asked upon meeting someone for the first time is, "How old are you?" This is because age is one of the factors for the determination of status, and it is important to know whether one should be respected as senior by, or should respect as a junior, this new acquaintance. Additional factors include education, wealth/income, position/rank, political connections, family ties, gender, etc., so one's status is not limited to age alone.
In the Bible, we see evidence for some of these cultural aspects sprinkled throughout in various stories. For example, in the story of Joseph meeting his brothers in Egypt (see Genesis 43:15-34), Joseph, of much higher rank (governor of all Egypt) and "an Egyptian," eats at a separate table from his brothers. He also arranges his brothers around their table in age order. Then Joseph does something that goes against the culture, just to see how the older brothers will react: he gives Benjamin, the youngest, the most favorable treatment. (The eldest should usually be the most favored.)
The status system is further reinforced by the forms of government which became most common in Bible times. Most Western civilizations today do not have a king, and have a voice in matters of government; but this was not the case in Bible times. The people were under the rulership of kings and governors who, for the most part, did not answer to the will of the people. The rulers' status gave them the power to dictate.
In this type of a society, one must be meek and subservient for as long as one is of junior rank. Once one has gained seniority, then it is the others who must be subservient. The common tendency within this type of culture is to look forward to and to covet that time of seniority, and there is frequently a certain amount of jockeying for position so as to obtain it.
Among the disciples, not only were the disciples themselves jealous for position, but also the mothers of some of them were desirous of seeing their sons promoted to positions of honor. Certainly, as noted in the question, pride is involved. But it should also be noted that the pride of their mothers is affected by the position which they have. If one's family member is of high rank, it elevates one's own rank within the society.
A Westerner might brag about his or her relative being famous or important, but in Eastern society it is not merely a matter of bragging rights: it literally affects one's day-to-day relationships with others. For this reason, status becomes more significant, and more emphasis is placed on it within the culture. And the disciples were no exception.
33 And he came to Capernaum: and being in the house he
asked them, What was it that ye disputed among yourselves by the way?
34 But they held their peace: for by the way they had
disputed among themselves, who should be the greatest. (Mark 9:33-34,
The disciples' actions were fairly normal for the environment in which they lived. The Pharisees engaged in the same spirit of "who should be the greatest," and the disciples were influenced by this. Jesus, however, was disappointed in them, for he had been teaching them from a different set of principles and their desires for self-aggrandizement showed they had not been learning their lessons.
Jesus took time at this point to emphasize the lesson he wanted the disciples to learn, with a live illustration.
35 And he sat down, and called the twelve, and saith unto
them, If any man desire to be first, the same shall be last of all,
and servant of all. 36 And he took a child, and set him in
the midst of them: and when he had taken him in his arms, he said unto
them, 37 Whosoever shall receive one of such children in my
name, receiveth me: and whosoever shall receive me, receiveth not me,
but him that sent me. (Mark 9:35-37, KJV)
Using a child to indicate who was the greatest was as nearly opposite to the disciples' thinking and culture as one could get. Children are junior in virtually every respect: they are younger, less educated, have no income or wealth, etc. This lesson must surely have made a lasting impact on the disciples' minds.