So duh, families change when one member of them is terminally ill. And we don't just mean that you suddenly have to cook your own dinner or keep trashcans in every room of the house for surprise barf sessions.
Conor needs to believe his mom will get better because he wants his family life to go back to normal. Only it hasn't been normal for a very long time. His relationships with his grandma and dad are uncomfortable to say the least; they're so different from him that they might as well be a different species (and to a British kid, Americans may very well be.) Yet because his mom won't get better, he'll need to rely on those relationships even more in the future. These tricky family dynamics are a big factor in shaping how Conor learns and grows throughout the novel.
This is going to sound like a corny joke from one of those unfunny kids' joke books, but when is a tree not a tree?
Conor's yew tree can take the shape of a giant person, with its branches turning into a body and its leaves turning into skin. It can walk, talk, and enter any room a person can. Then—bam—it can turn itself back into a tree. Conor doesn't need some human spouting off clichés to learn important life lessons—he's got an ancient fantasy creature to teach him instead. And as ancient fantasy creatures go, the Green Man is way more awesome than some boring old ghost or Sasquatch or something. Those dudes have been done to death.
The tree moseys on down from the graveyard to tell Conor it's seen ages unfold, from medieval times to the industrial revolution to the present day. It's got a whole root system full of universal stories about human motivation, like greed, revenge, and violence. And fear, of course, which is Conor's jam. By having someone who's not human comment on human behavior, Conor (and, therefore, the reader, a.k.a. you) gets a more objective view of what's happening in his head, heart, and life.