Would is being use in the sense of reason.
- What reason did she have?
- What caused/drove her to do this?
"Would" is a very powerful word in English. It performs many functions. Take a look at this link to see some of the ways it is used:
I agree with George French. In this sentence it is being used to ask what reason she could have for doing this. In other words, "Why would she do this?" is similar to "What motivated her?" It can also be said in a critical tone to mean: "What possible reason could she have to justify this action?"
I'd say did is more neutral.Hi, I don't get this difference. How about "why did she do this"? Does it not have the meaning of "what motivated her"?
I only know that "why would she do this" carries shock/disappointment that "why did she do this" doesn't.