Sounds like she's 'playing hard to get' (a fixation I'll never understand) judging by the wording.
It sounds like she does want to go out with you-going on the information I have now-but she's being playful about it. My advice is to ask again normally, if she does the same, smile, and ask what you do have to do. See where it goes from there.
However, if she said it angrily before, it might be because she's expecting you to be only asking so you can have sex. Are there any rumours/gossip surrounding you, or her, about a need for sex or some such thing?
In which case, it might be better to give up; once someone thinks about a rumour so much they reject something at face value, there's little you can do.
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