Better question: why do some people get wound up about it?
It’s not a sleight of hand, it’s not a double negative. It’s saying it wasn’t a problem for them. Some folks just wanna get mad.
My first thought when I hear “no problem” is:
“Well ain’t that just special!”
If you'd bothered to read the original Merriam Webster article, you'd have found you are incorrect:
"Parsing the expression, we have a joining of two negatives: no means "not any," and problem implies a difficulty in accepting something. Someone so inclined could deduce that a reply of "no problem" implies that one might have had a problem or difficulty with the task but in the end that wasn't the case, and for that reason only they're happy to have obliged."
From the article.