Professors have a right to say what they want in class, and students have a right to record them and expose them when they do.
The profs have the legal right to put in the syllabus that the lectures not be taped. End of story.
You're defending this horrible teacher and her thuggish union. That makes you an awful person.
If you say something in public, you have no right to restrict what those who listen do with your words. A professor expects you to take notes, essentially recording your words and "wisdom" If he/she is not wise enough to restrict themselves to what they would like the rest of the world to hear, they should learn to control what they say.
Recording lectures has been standard since portable reel to reels when I was attending college lectures nearly 50 years ago.