i can't not?

Yeah, you could say “I can’t not do it.” I’ve said this plenty of times. Number 2 is confusing.

I don't think your second sentence quite means what you think it means. In that example, you're saying that you were only able to do "it" because it was your duty. So if it wasn't your duty, you wouldn't have been able to do it. "I can't not do it" does sound weird, but that's just because double negatives aren't particularly common when there's an obvious way to make it a positive statement. However, that weirdness can be used as emphasis and I've seen that exact sentence many times and have even used it myself here and there.

Sometimes breaking a rule of English can be used to draw attention to a statement and put extra emphasis on something. In this case, it seems like "I can't not do it" might be the appropriate way to phrase things.

"I can't not do it." is perfectly fine as long as you're okay being informal. People say this frequently but it has a casual tone. A more advanced and formal way would be to use a verb that contains the negative concept you're going for, instead of using a double negative. English has many verbs that express not doing something. Picking the best one can convey a more nuanced meaning. - "I can't refuse." (Refuse means saying no to someone) - "I can't neglect my duties." (Neglect means not doing something you should do.) - "I can't ignore my obligation." (Ignore means to not give it any attention) Here's one that doesn't involve obligations: - "I can't resist eating another slice of cake." (Resist here means to overcome temptation and avoid something) You could actually say "I can't not" in any of these situations, but picking a great verb helps you sound more articulate.

Keep in mind that when saying "I can't not do it" aloud, people put emphasis on "not". "I can't \*not\* do it"

I would be more likely to say 'I've no choice but to do it', but 'I can't not do it' is perfectly fine.

I couldn’t but discharge my sacred responsibility.

Why do you "have to do in double negative form"? It's much clearer to say "I have to do it".

"I can't not do it" is perfectly acceptable, and would be the most common way to express this thought.

‘I can’t not do it’ is completely fine and used frequently. You could say it also as ‘I can’t skip doing this, it’s a requirement’ and have the same meaning. The second sentence means that the only reason you could do the duty, was because you had the job. It excludes everyone else from doing it because they’re not allowed to.

Spoken out loud “I can’t not do it” with emphasis on “not” is a completely natural way of expressing it. It seems strange in written form because of the lack of emphasis, which makes it appear on the surface to be incorrect by rule of redundancy, when the emphasis would make it clear that the double negative actually is necessary.

Number 2 means that, were it not your duty, you would not have been capable of doing it.

I can't do it means I cannot do it.