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.
A false dilemma fallacy is often paired with the Tu Quoque fallacy, to suggest, for example, if you can find something else that's wrong, then the argument is false, as if people can only work on one problem at a time, and if you don't solve problem A, then you can't work on problem B.
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).