Quote 1
"I'm not afraid in this way [of the sea]," said little Em'ly. "But I wake when it blows, and tremble to think of Uncle Dan and Ham and believe I hear 'em crying out for help. That's why I should like so much to be a lady." (3.72)
When Emily is rushing towards the sea, David admires her courage. But Emily isn't afraid of the sea for herself. She's worried about what the sea has done and will do to her family. Emily's father and uncle (Ham's father) were drowned, and this childhood trauma has strongly affected her development as a character. It's because of her sorrow at the loss of her family that Emily is so desperate to become a lady. She wants to have the money to protect Mr. Peggotty and Ham from their dangerous profession, fishing. And it's because Emily so wants to be a lady that she becomes vulnerable to Steerforth's seduction.
Quote 2
But there were some differences between Em'ly's orphanhood and mine, it appeared. She had lost her mother before her father; and where her father's grave was no one knew, except that it was somewhere in the depths of the sea.
"Besides," said Em'ly, as she looked about for shells and pebbles, "your father was a gentleman and your mother is a lady; and my father was a fisherman and my mother was a fisherman's daughter, and my uncle Dan is a fisherman." (3.57-8)
Emily is only, like, five years old at this point, but she already knows the important difference between herself and David. And it's not the difference you might expect – it's not gender difference. No, it's that David's father "was a gentleman and [his] mother is a lady," while Emily's father "was a fisherman and [her] mother was a fisherman's daughter." It's at this early stage that we learn what the primary organizing logic of this book is going to be. It's not going to be (mainly) about men and women. The primary divisions in this book are between the working, middle, and upper classes.
Quote 3
'Oh, pray, aunt, try to help me! Ham, dear, try to help me! Mr. David, for the sake of old times, do, please, try to help me! I want to be a better girl than I am. I want to feel a hundred times more thankful than I do. I want to feel more, what a blessed thing it is to be the wife of a good man, and to lead a peaceful life. Oh me, oh me! Oh my heart, my heart! (22.215)
When Emily meets poor Martha Endell, she foreshadows her own near future. In a fit of hysteria after seeing Martha, she promises that she wants "to be a better girl" than she is. She wants to be happy as "the wife of a good man" – Ham Peggotty. But like Steerforth himself, who also seems to recognize that he's doing something wrong by seducing Emily away, Emily appears to know the right thing to do. She just cannot bring herself to do it. It's like Steerforth is a whirlpool and Emily is caught in the current. What exactly compels both Emily and Steerforth to do the wrong thing, even though they know that they are doing wrong? Why can't Emily just choose to be "a better girl"? What's stopping her from being "a hundred times more thankful"?