Explain how the 1st half of the story is necessary to understand why Connie is vulnerable in the second half of the story. If this story is...

I think that the first part of the story lets the reader
inside the world of Connie's mind: not the way things are, but the way she sees them.
 Everything is about what she wants and what she believes. Her mother tries to get her
to see the world for what it is, but she rejects it: it doesn't fit with her sense of
her beauty and that of the world she has created in her
mind.

To avoid her mother and the world as she sees it,
Connie is sneaky and manipulative, putting her mother's fears to rest so Connie can hang
with an older crowd, something her mother would not knowingly let her do.  But Connie's
mom believes what Connie wants her to see, not what is
real.

There is an irony here.  Connie sees the world as she
wants it to be, and even though her mother fights the appearance of the world with the
realities of the world, Connie's mom comes also to see the world the way Connie wants
her to see it.  She believes her daughter's lies and tricks, and is lulled into a false
sense of security.  Connie has a false sense of security as well, but it is founded on
the fact that she sees nothing to be afraid of as she dreams her dreams and plays
pretend, as if she exists in a different world.

And then
the family sets off to go to an afternoon barbeque, leaving Connie home
alone.

When Arnold Friend arrives, Connie is startled.  At
first she is unsure of what to do.  She has no experience in knowing what the world is
really like because she has resisted all along what her mother has tried to tell her.
 Even as she starts to recognize the warning signals, they confuse her because she has
experience only with the world as she wishes it to be, not as it truly
is.

Arnold eventually talks Connie into just giving up.  He
uses the threat against her family to make her more vulnerable, but her confusion makes
the threat secondary.  Like a snake charmer hypnotizing a cobra, Connie cannot resist
his voice, cannot resist what she sees as the inevitable.  The will to fight leaves her
and she resigns herself to her fate.

Had Connie had a
better handle on the true world, perhaps she might not have been so vulnerable when
faced with the ugly truth about life and the dangers it holds: that
world is one she had never seen and could not, at last, even
imagine.

If I had to identify the point that breaks the
story into two parts, I don't think I would go with the obvious arrival of Arnold at her
house.  I think instead I would find the break where Connie distances her own behavior
from that of the Pettinger girl (the girl with a questionable reputation): Connie infers
that SHE would never be like "that dope," and then admits to
feeling sorry that she so cruelly tricks her mother with her lies.   The narrator
informs the reader that once again her mom continues to try to bring Connie out of her
fantasy world, but Connie's smooth and calculating lies seal her fate.  The real cruelty
will be her mother having to live with what happens to
Connie.

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Connie's mother kept dragging her back to the
daylight by finding things for her to do or saying suddenly, 'What's this about the
Pettinger girl?"

And Connie would say nervously, "Oh, her.
That dope." She always drew thick clear lines between herself and such girls, and her
mother was simple and kind enough to believe it. Her mother was so simple, Connie
thought, that it was maybe cruel to fool her so
much.