Tuck shot himself to prove to himself and his family, once and for all, that what they suspect to be the case, is, in fact true. It appears that, for some reason, the Tucks have become indestructable, and to prove it, he shoots himself to verify that nothing happens to him.
The Tucks have realized that something strange has happened to them. There have been a number of signs - Jesse had fallen from the top of a very tall tree, and "it didn't hurt (him) a bit." Then, their horse had been accidentally shot, and the bullet had gone right through him without "hardly even leav(ing) a mark." Then, "Pa got snake bit," and Jesse ate poison toadstools, and Ma Tuck cut herself, but none of them showed any sign of damage or hurt. The Tucks became aware that, while their acquaintances were growing older, they themselves were not, and then, when they return to Treegap, they come upon a tree that Tuck remembers cutting a "T" into many years before. The tree has not grown a bit, and the "T" looks as fresh as the day it had been carved. The Tucks remember drinking from a stream nearby; they and their horse had tasted of the waters, but their cat had not, and their cat alone had died after a long life some ten years before. The Tucks conclude that something about the spring water has apparently rendered them immortal, and to prove it, Pa Tuck shoots himself with his shotgun, and, sure enough, emerges unharmed (Chatper 7).
Tuck shot himself to be sure that they weren't immortal once and for all because of all the things that had hppened to the family but they still didnt get hurt. while the cat that did not drink out of the spring died.