Earlier quoted context omitted.
I'm not conceding that it's reasonable for a professor to answer something with "they should just know," but I think the issue here is that they seemed incapable of explaining it. It's one thing to say to a class "you should know how to $x, so I'm not going to teach it to you right now" but another entirely to be either unwilling or unable to explain exactly what they mean to a colleague.
Keep in mind that teaching is its own skill. Especially in universities, that skill can get awfully specific awfully fast. In particular, for a TT professor at an R1, odds are extremely good that they've NEVER taught anything below calculus and may have never even been the instructor of record even for calculus courses! They were hired to do research and teach graduate/upper-level undergraduate courses. Teachers that…
Admittedly, I was a math major in college, and was unaware of the existence of college algebra until I was hired to teach it.