If you make a good point with poor wording you weaken your point.
I just have a pet peeve, specifically, with people who redefine words in order to make their points.
Like anti-rants which base themselves on redefining whatever they're against to mean something horrible, when it actually doesn't.
In his case, sexism is genuinely really bad and it genuinely targets women, but it doesn't mean that the word means "male advantage". Men are usually at an advantage in regards to sexism, but that still doesn't mean that's what sexism, as a word, means.
Seeing as sexism can, and does, affect men (demonstrably) as well, it weakens his whole following point.
If you are saying something that is true, and is right, but you start it out by saying something that is demonstrably wrong, then it makes the whole of what you're saying seem less true, no matter how true and right the "actual" point is.
It's not just poor writing. It's more than that.