Focus of children's program
Typically for younger kids, parents' concerns and desired benefits are around physical fitness, self-regulation and perseverance, and some facet of the martial arts that links with self-confidence, a capacity against opposition, or sense or understanding of self-preservation.
As with any activity first of all, there is the relevance of perseverance or grit. It is natural foe any person, not just children, to be excited at the novelty of something the first 1 - 3 times, then become bored or discouraged, and quit after that. When a kiddo joins, they are suddenly confronted with unfamiliar faces, unfamiliar activities and movements, and unfamiliar routine. Whatever hesitation or anxiety we see in a new child is reasonable and normal, and not indicative of how it will be the 3rd, 4th, etc. session on.
That said, there is the first hurdle of "extending oneself" and trying: trying to copy what the teacher is showing, trying to do what the other kids are doing, trying to overcome one's own hesitation and anxiety. There are invitations and encouragements from the teacher and often other kids, but no one is forced to "extend themselves".
Next, as aikido is a physical activity, there is the relevance of physical self-awareness and movement competence. Every student develops their own sense of their respective body. As well they reconcile that inner sense with outer reality. One way is through watching the teacher and other students, and copying what they see.
Next, two points of aikido as a martial art:
One is, we do things like intentionally experience unbalancing and falling down. From individual exercises, this leads to improved and adaptive reactions to losing balance, and competence and confidence around controlling one's body. From paired activities, it leads to adaptive focus on one's own body, as opposed to over-focusing on the other person or loss of focus, such as by startle or fear reactions.
Secondly, we do much of our practice in pairs. There quickly develops a crucial comfort and familiarity with being touched. Additionally, one's sense of safety and confidence with being touched, as well as the respect and control (gentleness) of touching others is constantly being experienced and developed. There is also a "logic" that develops from practicing with others. Why does it make sense to move to this particular position? Why does it work better if you act on partner's elbow, not their shoulder? Why is it easier if you move at this particular moment, not before or after? As we practice, noticing and acting within these details is ever-present opportunity.