"On the other hand" without the first hand

Solution 1:

You are right, it is fine to use "on the other hand" without explicitly mentioning "the one hand" - the reader/listener can easily infer it.

Indeed, using "on the one hand... on the other hand" in most contexts sounds laboured and overwrought. It is sometimes useful to signpost to the audience in advance that you are going to supply an opposing view later, in which case it is useful - but for the most part it is better to leave the first part out.

In support of this: I spent a little time perusing the British National Corpus. It reports 5311 uses of "on the other hand", but only 1417 of "on the one hand". That would seem to suggest that "on the one hand" is only used roughly one third of the time, but in fact it's even less than that, because (judging from a random sample) most uses of "on the one hand" contrast it with "on the other" (or not at all) - so it's probably closer to one in four.

Solution 2:

"On the other hand" is a way of addressing the second part of a two-part problem or situation or solution. It does not have to be preceded by a sentence that states "on the one hand."

We have a great opportunity before us, as many have stated before. On the other hand, such an opportunity presents us with grave risks, so we would be wise to proceed slowly.

There is nothing wrong with that. "On the other hand" is simply another way of introducing a rebuttal to an idea, not an idiomatic formula. Your colleagues are trying to be over-consistent.

Solution 3:

It is fine to say "on the other hand" without saying "on the one hand" first if there was a first point that you are contradicting. You did imply that in your question, but I want to make sure about that.