Here's what is says about Times New Roman:

> Objectively, there’s nothing wrong with Times New Roman. It was designed for a newspaper, so it’s a bit narrower than most text fonts—especially the bold style. (Newspapers prefer narrow fonts because they fit more text per line.) The italic is mediocre. But those aren’t fatal flaws. Times New Roman is a workhorse font that’s been successful for a reason.

It says that there are problems. They're just not fatal.

> It even implores the reader with a bold "please stop". It makes no arguments to support this stance and offers no alternatives.

It says that there are plenty of alternatives (it specifically mentions Helvetica) that are better than Times New Roman. The argument is that Times New Roman is okay, but that it has flaws, and that there are easily available fonts that are superior. If someone is devoted enough to fonts to write a blog about them, then the existence of superior alternatives is enough of a reason to not use a font.