What is the difference between the following? Also, if both:
- in the other hand and
- on the other hand
are correct. And what is the reason?
On the other hand is a set phrase meaning "in a way that is different or opposite from the previous argument." (Source: https://www.collinsdictionary.com/us/dictionary/english/on-the-other-hand)
She might really love me. On the other hand, she might really hate me.
In the other hand is a valid, grammatical phrase, but it's not a set phrase. It only has its literal meaning, that something is literally in the other hand.
He took the basketball in the other hand as he drove to the hoop.
If you're still wondering "why," then you might need to have a better understanding of a what a set phrase is. Here are a couple of pages that explain this.