What are some quotes from To Kill a Mockingbird that display how growing up is portrayed by Harper Lee?

Lee portrays growing up as a growing understanding of and empathy for people, as well as a loss of innocence. 

The first important point in the growing up theme is the ability to see things from another person’s point of view.  When Scout goes to school, she immediately has a conflict with her teacher. The teacher is frustrated since Scout can already read and confused about Maycomb’s ways.  Scout's father explains to her that she needs to learn to understand things from another's perspective.

“…[If] you can learn a simple trick, Scout, you’ll get along a lot better with all kinds of folks. You never really understand a person until you consider things from his point of view-”

“Sir?”

“-until you climb into his skin and walk around in it.” (Ch. 3) 

As Scout matures, she finds herself in more situations that require trying to understand another person.  Her father's defense of Tom Robinson is unpopular, and Scout often gets caught fighting because she doesn't know how else to handle things.  She gets in trouble with her uncle about this, and explains to him that you have to listen to children before you punish them.

Well, in the first place you never stopped to gimme a chance to tell you my side of it—you just lit right into me. … an’ in the second place you told me never to use words like that except in ex-extreme provocation, and Francis provocated me enough to knock his block off—” (Ch. 9)

The concept of empathy is important to growing up.  As Scout matures, she develops a better understanding of others.  It is this empathy that helps her face down a lynch mob, appreciate Mayella Ewell’s circumstances during the trial, and understand what Boo Radley may be feeling. 

Another theme of growing up is the loss of innocence.  This is experienced by most of the characters, but Jem and Dill seem most profoundly affected by the trial.  Both boys are offended and shocked at the display of racism.  Dill, for example, gets so upset by Mr. Gilmer’s disrespectful treatment of Tom Robinson that he has to be removed from the courtroom. 

He later talks to Mr. Dolphus Raymond, one of the only people in town who isn’t racist. Raymond tells him that eventually Dill will get used to it.  

 “Things haven’t caught up with that one’s instinct yet.  Let him get a little older and he won’t get sick and cry. Maybe things’ll strike him as being—not quite right, say, but he won’t cry, not when he gets a few years on him.” (Ch. 20) 

Jem is also offended, but by the verdict.  He keeps believing that Robinson will be acquitted right up until the end.  When he learns that the jury convicted him, he feels betrayed.  It is a lesson in how deep racism goes.

I shut my eyes. Judge Taylor was polling the jury: “Guilty… guilty… guilty… guilty…” I peeked at Jem: his hands were white from gripping the balcony rail, and his shoulders jerked as if each “guilty” was a separate stab between them. (Ch. 21)

Scout and Jem also face the loss of innocence when they fear for their father's life. Bob Ewell threatens Atticus for insulting him during the trial.  Eventually, he attacks the children as they are coming home on Halloween. Boo Radley saves them, and it is as if Scout and Jem's childhood has come full circle.