B1 point 4 in DISCOURSE MARKERS and in writing is defined as:
ORGANISING with a range of phrases as discourse markers to introduce contrasting statements.
The English Grammar Profile examples listed are:
‘on the one hand’, ‘on the other hand’ and ‘on the contrary’.
They seem to start sentences more often than not.
Ngrams from iWeb corpus:
1 . ON THE ONE HAND, THERE IS THE 86
2 . ON THE ONE HAND, IT ‘S A 69
3 . ON THE ONE HAND, THERE IS A 62
4 . ON THE ONE HAND, YOU HAVE THE 59
5 . ON THE ONE HAND, WE HAVE THE 52
6 . ON THE ONE HAND, YOU WANT TO 47
7 . ON THE ONE HAND, IT IS A 43
8 . ON THE ONE HAND, THIS IS A 34
9 . ON THE ONE HAND, THERE ‘S THE 31
10 . ON THE ONE HAND, YOU HAVE A 31
There seems like more conditionality with ‘other’ which is also much more common:
1 . ON THE OTHER HAND, IF YOU ARE 1023
2 . ON THE OTHER HAND, IF YOU HAVE 729
3 . ON THE OTHER HAND, IF YOU ‘RE 663
4 . ON THE OTHER HAND, IF YOU WANT 469
5 . ON THE OTHER HAND, IF YOU DO 411
6 . ON THE OTHER HAND, THERE IS A 269
7 . ON THE OTHER HAND, I DO N’T 239
8 . ON THE OTHER HAND, THERE ARE SOME 208
9 . ON THE OTHER HAND, THERE IS NO 200
10 . ON THE OTHER HAND, IF IT IS 171
1 . ON THE CONTRARY, IT IS A 112
The wheelchair is not a failure, on the contrary, it is a tool of freedom.
2 . ON THE CONTRARY, IT IS THE 90
3 . ON THE CONTRARY, THE COOLEST MONTH 64
4 . ON THE CONTRARY, THERE IS A 50
5 . ON THE CONTRARY, I BELIEVE THAT 32