Because darum translated into English means for that "reason" or because of that not about that "subject" So the sentence means For that reason (maybe therefore?) I won't ask you. One more example Darum ging ich nicht in der Schule gestern = That's why I didn't go to school yesterday.
It replaces the preposition and pronoun ("for it/that"). It's called a "da-compound" and you can make them out of many prepositions to make things like "with it/that," "for it/that," etc. This website explains them in detail, if you want to know more: http://www.lsa.umich.edu/german/hmr/Grammatik/Da/Da.html
I think that might just be because other compounds ("damit," "dafür," "daran," etc.) are more common, at least I know I've seen those more often than some others. I tried thinking of more situations where "darum" would be used, but I can't think of any other verbs that use "um" other than "handeln um." Really, they're all used in pretty much the same ways (replacements, anticipatory) so I think it's okay that a detailed example wasn't given for every single one that exists.
"Ich werde dich nicht darum bitten."
Does this (German sentence) mean "I will not question you about that [subject, situation, whatever]? " or "I will not ask you to give me that [favor, help, repayment, whatever]." ??
The use of "darum" suggests the former meaning, but in English one would say "ask about that", not "for that." If the latter is meant, then I would have thought "dafuer" would be more appropriate. Can anyone clarify?
After all, I could not write down exactly what was being spoken, but I think my German sentence is itself not wrong, is it, although the meaning is different from the original German sample.
Ich werde dich nicht darum bitten.
Ich werde dich darum nicht bitten.
The question is (1) where to put "nicht", whether in front of "darum" or in fron of "bitten. and (2) what you want to emphasize.
This advice and learning is working great for me in writing but for the life of me I can't figure out how I'm going to stand next to someone and have a speaking conversation because the word order dissection in my mind would be awful! I'm thinking I might have to have written conversations and claim in hard of hearing.