As the interviewee: "Why would I not want to work at this company"
Recruiters like this question
It is an easy way to get a view of the culture of a company (if you don't like to work agile) or what there biggest issue is (it can get very political) and so I can decide for myself if I like that or that it would be something that will eventually make me leave. If someone says they don't know, it's a red flag.
As the interviewer: "Why would you not work at this company"
To see if they understand the kind of company it is and what the challenges are, also I find the answers more honest and thoughtfull than asking: why would you want to work here.
So they will think why they want to work with us.
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As the interviewee: "Why would I not want to work at this company"
As the interviewer: "Why would you not work at this company"