[Vocabulary] What does "I wouldn't do either" mean in this sentence?

[Farshad.021]

Hey guys, hope you are doing great,

Dear friends, I was watching a movie last night and there were some sentences that I couldn't understand their meanings properly. I'm going to ask one of them here but first I'll give a context:

Mary, Zoe and Jenn are playing "would you rather" game.
Mary asks Jenn: Would you rather watch your mom get murdered by your daddy or get raped by your daddy while your mom had to watch?Jenn says: I guess get raped by my dad.
Zoe says: Oh, gross!
Jenn says: What? Would you rather have your mom die?
Zoe says: I wouldn't do either.

Now, my question is about "I wouldn't do either". Is that "do" referring to "rather" or something? If yes, so does Zoe mean "I would rather none of them"?

Sorry if my question might seem a bit odd.

Thanks in advance,

 

[Grumpy]

Zoe means that she would rather not participate in either of the two scenarios.

I agree with Zoe...