relationships. 

There are some benefits to living forever. Jesse and Miles travel and experience the world, and have the opportunity to see it change. Mae and Angus live comfortably, as they are experts at crafts they can sell to live off of. They live a mostly relaxed and quiet existence. 

The Tucks do their best to prevent anyone else from finding out about the spring or accidentally drinking from it. It is hidden by pebbles. Winnie Foster only found out about it because she saw Jesse drinking from it. Since he was already immortal, it wouldn’t hurt to quench his thirst. 

The Tucks kidnap Winnie to prevent her from drinking from the spring, and so they can tell her the whole story. They explain how everyone but the cat drank from the spring, and they later realized they could not be hurt or die. Mae Tuck tells Winnie this is why she should not drink from the spring. 

"And we figured it'd be very bad if everyone knowed about that spring," said Mae. "We begun to see what it would mean." She peered at Winnie. "Do you understand, child? That water—it stops you right where you are” (Chapter 7).

Angus also explains that the Tucks have been removed from the normal wheel of life. This is what makes it a little tiring for them. They do not get to age and die like everyone else. 

Jesse has a different perspective. He is the youngest Tuck, and never got to have a family like Miles because he was only seventeen when he drank. He knows he can’t marry a normal, mortal woman. Miles’s wife and children left him because they thought he was cursed by the Devil. Since Winnie knows about the Tucks, Miles asks her to wait until she is his age and then drink the water so they can get married, but she decides not to do so. 

The Tucks return much later to learn Winnie lived a normal life and died at a respectable old age. They understand why she made the choice she did. Not everyone wants to live forever, and the Tucks wish they had known what was in that spring.

By "Tuck" I believe that the question is referring to Angus Tuck. Chapter 12 contains the answer to this question. It is during this chapter that Angus takes Winnie out onto the pond in order to talk to her about what exactly immortality means for him and his family. It is clear that Angus is not excited about being immortal, and it is also clear that he thinks nobody else should have his gift/curse.  

Angus Tuck uses the stream's current as an analogy to explain to Winnie why being immortal is not right or good: 

"Life. Moving, growing, changing, never the same two minutes together. This water, you look out at it every morning, and it looks the same, but it ain't. All night long it's been moving, coming in through the stream back there to the west, slipping out through the stream down east here, always quiet, always new, moving on. . . Always coming in new, always growing and changing, and always moving on. That's the way it's supposed to be. That's the way it is."

Life's constant change is important to Angus, and he is no longer a part of that natural life cycle. He explains to Winnie that he is no longer a part of the "wheel," and he does not like it. He admits to Winnie that he would love to once again be a part of that wheel. Winnie does not understand why. She cannot fathom why anybody would want the ability to die. Angus gives a simple and wonderful explanation as to why he really does not like being immortal anymore. In his opinion in order to know that you are living, there has to be the possibility of death. Since he cannot die he does not feel that he is really living. He just is. To Angus his "life" is like that of a rock. It cannot die, because it is not alive. It is just stuck in time:

"Being part of the whole thing, that's the blessing. But it's passing us by, us Tucks. Living's heavy work, but off to one side, the way we are, it's useless, too. It don't make sense. If I knowed how to climb back on the wheel, I'd do it in a minute. You can't have living without dying. So you can't call it living, what we got. We just are, we just be, like rocks beside the road."

Several reasons come to mind as to why Tuck might not like the idea of living forever in Tuck Everlasting by Natalie Babbitt. Many of us think that the idea of immortality is intriguing, but if we stopped and really thought about it, we just might change our minds. Tuck already has figured out some of those things. If he falls in love, for example, and his love ages naturally and someday dies, he will watch all this as his young self. He watches people come and go throughout time.

He and his family also have to be fairly constantly on the move to avoid being "found out." If they stay in one place too long, people are going to begin to notice that they never age. How hard it must be for Tuck to feel he can never get too comfortable anywhere, to never be able to get to close to anyone lest they discover his "secret." At one point in the book, the author writes,

"For some, time passes slowly. An hour can seem like an eternity. For others, there was never enough. For Jesse Tuck, it didn't exist (Babbitt).

While the world changes around him, Tuck will remain unchanged. That would have to be difficult to accept.