wouldn't "on the other hand" be a better translation for: por otro lado?
"Por otro lado" can either mean "on the other hand" (as a contrast connector) or "in addition" as an "adding ideas" connector. In this case, you saw the meaning of por otro lado in this list for connectors that are used to organize and add ideas, but in this other list for connectors used for contrasting ideas you can see this other meaning of "on the other hand".
I hope it clarified it.
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