The motivation for this question came from this Software (C#) question
"Why is it faster to check if dictionary contains the key, rather than catch the exception in case it doesn't?"
"On the one hand, throwing exceptions is inherently expensive, because the stack has to be unwound etc. On the other hand, accessing a value in a dictionary by its key is cheap, because it's a fast, O(1) operation. ..."
Well, on one hand, the hands illustrate different points, (but/however) on the other hand they are both supportive of the original question "why is it faster..."
I thought the idiom "on the other hand" can be replaced with "but" or "however".
But for this case that appears not to be true and the idiom would need to be replaced with something like "additionally."