Why is it so important for Jerry to swim through the tunnel?

Like many kids of his age, Jerry wants to be able to do whatever the older boys do. In fact, he views being able to swim through the tunnel in the huge rock as a rite of passage.
Initially, for Jerry "to be with them, of them, was a craving that filled his whole body." He yearns for acceptance by the older boys. At first, when the others wave and smile at him, Jerry is content because the group seems to have accepted him. However, when they dive and come up on the other side of a dark rock, Jerry again senses alienation.
Jerry at first feels accepted, but when the older boys swim through the great rock, a feat that Jerry cannot do, he feels their rejection since he recognizes that they perceive him as juvenile. The boys' ability to hold their breath and swim through the great rock can be likened to scaling a cliff or making one's first successful dive off the high board. In short, it is a feat that allows them to perceive themselves as more men than boys. Jerry wants to be perceived as more than just a boy as well.
After he is humiliated by the older boys, who swim away, Jerry resolves to be able to perform the feat of holding his breath and swimming through the tunnel. When he is finally successful, "he did not want them. He wanted nothing but to get back home and lie down . . . . It was no longer of the least importance to go to the bay." Jerry does not "want" the other boys because he has proven to himself that he is now their equal by completing his rite of passage.

It is important for Jerry to swim through the tunnel, on a literal level, because he wants to be able to fit in with the older, local boys who could do it.  These boys seemed "like men to Jerry," and when they came to the wild bay, he wanted nothing more than to be accepted by them.  Initially, the boys made room for him, but once they began to swim through the tunnel, he clowned around to get their attention, and they abandoned him.  In Jerry's eyes, what really separates him from them is their ability to perform this physical feat.  He longs to close the gap between himself and these older boys by erasing this difference.
On a symbolic level, Jerry wants to swim through the tunnel because he longs to grow up.  Swimming through the tunnel feels like an initiation of sorts, as if accomplishing this task will prove, somehow, that he's ready for adulthood.