Treat 'convince me' as a request to strengthen your reasoning first, not as a signal that you need to reverse your conclusion.

Interviewers may pressure-test whether your recommendation is supported by the analysis. Changing your position immediately can make it look like you do not trust your own reasoning, while refusing to reconsider anything can look rigid.

Restate the recommendation, cite the two strongest pieces of evidence, and acknowledge the main risk. If the interviewer then introduces new information that changes the economics, update your answer explicitly.

Practice defending recommendations in a simple sequence: conclusion, evidence, risk, condition for changing your mind. That gives you a stable response when an interviewer pushes back. If useful, this guide on communication under pressure gives more detail.

I used to change my answer the second they pushed. Bad habit lol.