C.S. Lewis loves his gender roles. And, as the oldest girl among the four children in Narnia, Susan often takes on a motherly role. (For example, it's Susan who makes the practical suggestion that the children put on the fur coats from the wardrobe to keep them warm in the snowy landscape. We're surprised she didn't hand them granola bars and hand sanitizer.)
Sometimes Susan's mothering is annoying to the others. On their first night in the Professor's house, Susan tries to tell Edmund that it is his bedtime, and Edmund immediately retorts:
"Trying to talk like Mother […] who are you to say when I'm to go to bed? Go to bed yourself." (1.7)
Although Edmund is a snarky little pill, there's an important truth behind his criticism. Susan is definitely playing house.
In her hurry to grow up and act like a grown-up, Susan often forgets that she's also just a kid. Before she experiences Narnia for herself, Susan is ready to believe that Lucy might be losing her mind. And when the Professor suggests that other worlds could really exist, she's confused because:
She had never dreamed that a grown-up would talk like the Professor and didn't know what to think. (5.28)
Susan clearly equates "growing up" with being practical, literal, and maybe even a little unimaginative. She's in such a hurry to become an adult that she hasn't stopped to think about the more amazing possibilities that the world holds.
In many situations, Susan shows that she is the least courageous of the four children. When she finally does make it into Narnia and discovers—along with Peter, Edmund, and Lucy—that Mr. Tumnus has been arrested, she says,
"I wonder if there's any point in going on […] I mean, it doesn't seem particularly safe here and it looks as if it won't be much fun either. And it's getting colder every minute, and we've brought nothing to eat. What about just going home?" (6.42)
We're pretty torn about what to think about Susan's attitude. When we're reading The Lion, the Witch, and the Wardrobe at home, curled up in a chair with a cup of hot chocolate, it's easy to think that Susan is dull and unadventurous. But if we were really in Narnia, standing in the snow with no food, and we had just found out that the only friend we had there had been arrested by an evil Witch…we might want to go home, too.
Besides, Susan's lack of courage doesn't prevent her from sticking to her values. After a discussion with Peter, Susan, and Edmund about what they should do, she admits,
"I don't want to go a step further and I wish we'd never come. But I think we must try to do something for Mr. Whatever-his-name is – I mean the Faun." (6.56)
We also notice that Susan isn't afraid of Narnia in particular—she is afraid of the unknown in general. At the end of the book, after she has reigned as Queen Susan the Gentle for many years, Susan, along with the other children, is led by the White Stag to the lamp-post in the woods. The other three want to see what lies beyond it, but Susan doesn't:
"By my council, we shall lightly return to our horses and follow this White Stag no further." (17.34)
So, no matter what world Susan is in, she's nervous about crossing its boundaries.
Of course, Susan does have virtues, and she does develop a special connection with Aslan, much in the same way that her sister Lucy does. Susan notices Aslan's depression on the night they leave the Stone Table, and with Lucy she follows him as he trudges sadly toward the place of his sacrifice. Like Lucy, she comforts him on the night of his death, burying her hands in his mane, and, like Lucy, she witnesses his murder and mourns for him all night. Susan romps with Aslan after his resurrection and helps him free the statues at the Witch's house.
When the children become Kings and Queens of Narnia, Susan becomes Queen Susan the Gentle:
[...] a tall and gracious woman with black hair that fell almost to her feet and the Kings of the countries beyond the sea began to send ambassadors asking for her hand in marriage. (17.21)
Susan's virtues, however, are more passive than Peter's, Edmund's, or Lucy's. While Peter is a great warrior, Edmund is a wise judge, and Lucy is brave and cheerful, Susan is simply gentle and pretty. Those are good things to be, but she doesn't seem to be very actively good—she doesn't seem to take action herself, but to be good and practical in the background.
One of her gifts from Father Christmas hammers this passivity home: she receives a magic hunting horn which, when sounded, will call help to her no matter where she is. Wouldn't it be just a little bit cooler if she got a magic sword and could help herself? Of course, she does get a magic bow and arrows—and, if you keep reading the Narnia books, you'll find out that she becomes a pretty great shot.
If you're thinking that Susan got the short end of the stick, then we totally agree with you. C.S. Lewis, as the author, doesn't really give Susan much of a chance. We don't want to make you read any major spoilers, but let's just say that in the rest of the Narnia books, Susan continues to get shafted. If you want to read a 21st Century story that grapples with this issue, then you should check out Neil Gaiman's 2004 short story "The Problem of Susan."