Is this correct to use "on the other hand" or should I use "in contrast"
Self-face concern is the concern for a person’s own image. Other-face concern, on the other hand, is the concern for another’s image. Mutual-face concern is the concern for ...

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Answer

Both work, and what you have said certainly makes sense. Which one you use depends on the formality of what you are saying though. 'On the other hand' could be seen as a less formal alternative to saying "In contrast."

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