Coming out of an airport, you have to pick one of two exits: "Goods to Declare" or "Nothing to Declare". You have to go through one to get out; but (at least in Customs' eyes), by going through either exit, you state whether or not the contents of your luggage are legally subject to import duties. If you feel so scrupulously honest and so intensely secretive that you decide you have to leave that question unanswered - your only option is to stay inside.
Often your language does that too (Whorf said it first.) Just like the airports, the trick is to set things up in such a way that trying not to answer the question is either unacceptable (ungrammatical) or automatically interpreted as implying a particular answer. If you're talking about a friend in English, you don't have to indicate whether the friend is male or female until you refer back to the friend with "he" or "she"; in Arabic or Spanish, you have to state which it is from the start; and in Chinese or Songhay you can get away with never saying it at all. If you believe something definitely happens at some point, but don't want to say whether it's already happened or not yet, there's no simple way to say that. At best, you end up having to use cumbersome disjunctions like, if you're into apocalyptic prophecies, "The Antichrist either will be born some day or already has been"; and disjunctions like that will always be interpreted as meaning that you don't know which, not that you know but don't feel it's relevant.
In Korean (according to a talk by Peter Sells I heard today), a special verbal affix -si- (one among many, many politeness indicators) is used to indicate that the human subject of the verb (loosely speaking - it may also be a possessor of the subject, or a topic) is notionally of higher social status than the speaker. Thus:
"The teacher went."
"The cat went."
The thing is, this means you can't be neutral about the subject. If you don't use this suffix with a subject that would normally take it, like "teacher" or "pastor", your listener will assume that you don't respect them so highly. You can't even get away with being ambiguous - I'm told that a disjunction of politeness levels, like *"The teacher went(honorific) or went(unmarked) away", is totally unacceptable. There are genres, such as academic writing or journalism, where politeness morphology is not normally used, allowing you to be neutral on this; but in a face-to-face conversation, as far as I understand, no such solution is available. (Any Korean readers should feel free to correct me!)
No language is likely to be able to stop you from saying what you want to say, if you try hard enough. But things like this can make it a lot harder to avoid saying what you don't necessarily want to say.