WALTER: You can marry all you want to, Hildy, but you can't quit the newspaper business.
HILDY: Oh! Why not?
WALTER: I know you, Hildy. I know what quitting would mean to you.
HILDY: And what would it mean?
WALTER: It would kill ya.
HILDY: You can't sell me that, Walter Burns.
WALTER: Who says I can't? You're a newspaperman.
HILDY: That's why I'm quitting. I want to go someplace where I can be a woman.
WALTER: You mean be a traitor.
HILDY: A traitor? A traitor to what?
WALTER: A traitor to journalism. You're a journalist, Hildy.
Being a newspaperman (not a newspaperwoman, note) is contrasted with being a woman. Both Walter and Hildy seem to think there's a disconnect between being a woman and having a career. This is perhaps the root of Hildy's misery; if she, and those around her, could admit that women can have careers, she woudn't be so torn up about it.