I have always been told that you can't use on the other hand without first using on the one hand. But I often see on the other hand used alone. Has this rule changed?
On the one hand, sometimes you need to pair these two phrases. On the other hand, sometimes you don't.
You use these conjunctive adverbs to contrast two ideas. If you start your sentence with on the one hand, then you must pair it with on the other hand to introduce the second idea.
Incorrect: On the one hand, I love the freedom of working freelance. But I crave the financial security of a full-time job.
Correct: On the one hand, I love the freedom of working freelance. On the other hand, I crave the financial security of a full-time job.
However, Garner's Modern American Usage (2009) and Collins Cobuild English Dictionary for Advanced Learners (2001) agree that it isn't always necessary to pair on the other hand with on the one hand. You can use on the other hand alone to create a smoother transition between sentences.
Correct: I love the freedom of working freelance. On the other hand, I crave the financial security of a full-time job.
Note that these phrases can make your writing heavy. Often, you can leave them out:
I love the freedom of working freelance, but I also crave the financial security of a full-time job.