As a non native speaker of English, I have a hard time putting an equal sign between "Things are a bit sticky" and "[we are] in extreme difficulty"
Are these sentences really similar to a British English speaker?
To me the first one means "we have some minor issues" if talked literally, or "we have bigger issues but I decided to add a layer of nonchalance so that you miss the point"
In most contexts, you are correct that the translation of "Things are a bit sticky" is typically not interpreted as "We are in extreme difficulty."
However, in that specific case, the British general supposed that it was the point of pride for a British officer to rarely admit a weakness or lack of control over a situation. So, the slightest admission of the circumstances being "a bit sticky" should have been a sign that circumstances were severe, or otherwise he would have avoided making any admission at all.
The less ambiguous way—which would have avoided any ambiguity due to the general's understatement—would have been for him to state the facts: his troops were substantially outnumbered, and therefore they could only realistically last a short amount of time without support or withdrawal. However, perhaps, it is possible that he could not send a message of that length in the circumstances of the time.
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I took a brief look at your profile to try and guess your native language to make a comparison, and it appears you may be a francophone.
A perhaps similar example would be if you ask someone « Ça va ? » ("How goes it?") and the other person responds by saying: « Ça va... » ("It goes..."). For some people, « Ça va » is their default response, so it means that their situation is no different than usual. For others, who you might know to usually say the chipper response « Bien ! Et toi ? », a sudden change to « Ça va... » may be a hint that things aren't going so well, and a way to avoid directly saying « Non, rien ne va et je suis déprimé » (as taken from [1]).
The British general's phrase therefore had a distinct literal meaning, but he meant for the phrase to carry a different message that he expected the US general to pick up on (which did not happen, as the US general interpreted the phrase by its literal meaning instead).
As for "ça va": if I had a tumor dangling from my leg and went to the doctor, I could answer when asked "comment ça va?"
- "ça vaaaaaaa...." because I am a Real Man (TM) who does not show weakness, but I should suck it up and cut the tumor myself instead of coming and whining. And only hope that the MD would probe me until I talked about the "sticky thing" that weights 15 kg and makes me turn right when I walk. I should not have come to the MD at all
- or say what I have because I came for that.
By their logic, I do not understand why the British admitted to any problems, putting their honor in jeopardy for the small reward of maybe having their lives saved (and the lives of the people under the general who maybe had a different view on their future).
Are these sentences really similar to a British English speaker?
To me the first one means "we have some minor issues" if talked literally, or "we have bigger issues but I decided to add a layer of nonchalance so that you miss the point"