The term false dichotomy fallacy (or fallacy of the false dichotomy) is typically used when a person concludes that your position is B because you commited to the view "not A", but there is at least one other position (C, D, E . . .) one can take. For example, when you say that a certain human trait is not 100% environmentally determined, people will often assume you think it is 100% genetically determined, despite the fact that there are a lot of numbers between 0 and 100. In so doing, they are committing the false dichotomy fallacy.
This fallacy, or a variant of it, can be committed even if there are only two possible states of the world. Suppose someone was about to toss a coin and declared: "This one will certainly come up heads." You might then say, "I wouldn't be so sure about that" and the person might reply, "Oh, so you think it will come up tails?" In this example it's obvious: You didn't mean that the other state of the world is certain to come to pass, you simply meant to express uncertainty, given that we cannot know the result of the coin toss.
While the example is a bit far from most real-life situations, variants of it seem to come up quite frequently. Generally, your expressing doubt that X is true is likely to be read as your asserting that X is not true. People tend to go about as though one had to take a confident position on as many issues as possible and assume others feel the same way. (In U.S. discourse, "opinionated" is usually meant as a compliment.*) This may be a sign that uttering opinions has little to do with truth-seeking an a lot with positioning oneself in social space by signaling what type of a person one is.
*Until a few minutes ago, I thought that there was no term in German for the word "opinionated". Now I see that the dictionary I consulted gives two terms that are clearly negative, eigensinnig and starrsinnig.