There are two aspects to the non-believers that Mormon cites. The first of these is that they "could not understand the words of king Benjamin, being little children at the time he spake…."
This is an interesting passage, because it places Benjamin at a particular point in time. Why was not Benjamin's teaching reinforced? Why did it matter that they did not understand it when they were small?
The answer might lie is the power of the situation which transcended his words. We know king Benjamin's speech as powerful today, but in the context of the time and place, it must have been overwhelming. Indeed, the reaction of the people described underscores the power of the speech to move the heart. The small children would not have been as cognizant of what they felt at that time. While their parents would have been unable to deny what they felt, the children had no such powerful memory on which to rest their belief.
The second answer is more literary. Mormon is making a contrast between the teaching of the past prophets and the teaching of subsequent generations who believe on their words.
Significantly, Mormon's second reason that there were unbelievers was that they "did not believe the tradition of their fathers." Certainly their fathers had attempted to teach the things that they had heard and felt, but with equal certainty there were those of the rising generation who listened to other influences, and who dismissed some of the teachings of their parents.
Certainly there are many in this modern world who can easily attest to the tendency of some children to go their own way - regardless of the passion and conviction with which their parents teach what is in their hearts.
So were these children. Mormon tells us that they were too young to have had the personally transforming experience that their parents had undergone, and that they had elected not to believe in the teachings of those parents.
Literary: Remembering that in the original Book of Mormon this verse followed immediately after our current Mosiah 25:24, we should understand that this text is an introduction to a subject that is designed to be diametrically opposed to the information which preceded it. In the immediately preceding passage, we have the establishment of the church, and an apparent picture of unity of purpose.
Here we have the contrast. The text makes if fairly clear that this division in belief was already present in Zarahemla prior to the arrival of Alma and his conception of church. Nevertheless, it is placed in contrast with that story because the essential tension will be between these non-church Zarahemlaites and the churched Zarahemlaites. By presenting the stories in this manner, Mormon structurally highlights the social tension by his placement of the literary tension.