How does Winnie’s talk with Miles when they go fishing relate to her earlier talk with Angus in Tuck Everlasting?

Winnie discusses the downsides of immortality and why everything needs to die someday with Angus and Miles.

The Tuck family is immortal.  Winnie stays with them while they explain to her how they became immortal and why she should not drink the water and become immortal herself.  She has conversations about immortality with both Angus and Miles.

Angus explains to Winnie that being immortal is not all it’s cracked up to be.  When you are immortal and no one else in the world is, you are not fully experiencing life.

That's what us Tucks are, Winnie. Stuck so's we can't move on. We ain't part of the wheel no more. Dropped off, Winnie. Left behind. And everywhere around us, things is moving and growing and changing. (Ch. 12) 

If Winnie were to drink from the spring, she would become stuck too.  She would be a little girl forever.  It would be the same problem that Miles has, and especially Jesse, because when you are a child forever you really miss out on important things in life.

Winnie tells Miles that she wishes nothing had to die.  Miles, who can’t die, explains to her that there is a reason for death.

"Well, now, I don't know," said Miles. "If you think on it, you come to see there'd be so many creatures, including people, we'd all be squeezed in right up next to each other before long." (Ch. 17)

Miles tells Winnie that things kill and die.  This is the natural way.  When they catch a fish, she makes him put it back.  He understands why she does not want to see the fish die.  She still wants to believe that everything can live forever, even though she knows why it shouldn’t.

Miles tells Winnie that he wants to do something important eventually.  She understands this sentiment.  Miles has all the time in the world, and he wants to make it matter.  Winnie wants to become someone.  Before she was “kidnapped” she wanted to go on an adventure.  Now she has had one.