Your Fallacy Is
(Also known as: "False dichotomy", "False trichotomy", "Fallacy of Excluded Middle", "Black-or-White")
Citing one side of an issue and using it to suggest any/other side is invalid.
In reality, the world is not "black and white." Just because one thing might be true, does not mean its opposite is un-true.
Some people would argue that if they can show you something that contradicts your claim, this validates their opposite claim. That's not valid. Instead, this is a technique to mislead and distract, as well as over-simplify the issue.
In reality, there are shades of grey. Things aren't black and white. There can be many solutions to a problem, and there can be many issues on all sides. Do not let someone dismiss your claims by citing a contrary truth (which is often cherry-picked).