To me, this is a way for Jerry to show that he is independent.
If you look at what his life must be like, you can see why he would want to go to join the boys. He seems to be the only child of a single mother. His mother seems to be a bit overprotective of him. I think that young kids always want to be more independent and a boy in this situation would want to even more than normal.
So I think that he wants to go join the older boys to show that he is independent and that he is able to be accepted by people who are more of his peers.
The boy in the short story "Through the Tunnel" is only eleven years old and stuck with his mother. Like all other boys he wants to make friends and do something fun and exciting. His mother is content to sit o the beach and read.
The boy also sees that the boys are a group of friends and he feels left out. He wants to be a part of their group and do what they are doing. When they disappear under the water his curiosity gets worked up. Once he realizes what they are doing, he wants to be able to demonstrate that he can make it through the tunnel and prove to them that he can hang with them.