First Person Can Be* Intimate
*emphasis on "can be"
When people say first-person is intimate they are probably thinking about a book like, The Catcher In the Rye (Salinger).
Reading the first couple of sentences is very instructive (and compelling):
If you really want to hear about it, the first thing you'll probably
want to know is where I was born, and what my lousy childhood was
like, and how my parents were occupied and all before they had me, and
all that David Copperfield crap, but I don't feel like going into it,
if you want to know the truth. In the first place, that stuff bores
me, and in the second place my parents would have about two
hemorrhages apiece if I told you anything personal about them.
It's as if you are really sitting and listening to a teen-aged kid who is letting you inside. That's what people think of when they think of first-person.
S. E. Hinton was another great writer of first-person narratives.
Check out the intro to The Outsiders.
When I stepped out into the sunlight from the darkness of the movie
house I had only two things on my mind: Paul Newman and a ride home.
I was wishing I looked like Paul Newman -- he looks tough and I don't
-- but I guess my own looks aren't so bad.
Not Just Listening to Talk, But Experiencing Feelings
Again, this kind of writing is fantastic when done by great authors. And it does create a kind of intimacy with the character because you're not just listening to the character but you're sitting inside his head and knowing exactly what it feels like to be him.
Modern Problem With First-Person
The problem that has occurred with first person more recently is that amateur authors jumped on a band-wagon of the past success of these type of novels and started writing everything in first person.
First Person Can Sound Egotistical
However, first person is not a guarantee that the writing will be more intimate. Often if falls into other problems which make the character simply sound egotistical.
It can also become extremely overwhelmingly annoying as the reader is forced to listen to long monologues coming from a character who can't seem to shut up. This is the case when you have a poor writer deciding to use first person because it is easier.
Yes, sometimes first person is chosen because it is easier.
First Person May Be Easier
Here's what I mean. As humans, we all think in first person so many new authors think,
"Hey, I'll just write down what I'm thinking and I'll have a novel."
That is not an effective way to choose POV.
Third Person Can Be Intimate, Maybe More So
You could write a very intimate version of your story in third person by moving close to one character.
For example, if we re-wrote The Outsider's excerpt in third person you don't lose a whole lot and you could gain some possibly.
When Ponyboy stepped out into the sunlight from the darkness of the
house he had only two things on his mind: Paul Newman and a ride home.
He was wishing he looked like Paul Newman -- Newman is tough looking and Ponyboy has a softer chin
-- but he's a good looking kid.
Couple Of Reasons For Choosing Third Person
There are other things you can tell the reader about your main character that won't sound egotistical in third person and you can tell more of the story than you can from the limited viewpoint of a first person character.