Here, then, is my theory as to why most professors who object to their class lectures being recorded do so:
They fear having what they say exposed to the general public.
Why Professors Object to Being Recorded
After the election of Donald Trump as president, a professor at Orange Coast College in California, Olga Perez Stable Cox, went into an extended hate-rant against the president-elect. Among other things, she described the Trump election as an “act of terrorism,” labelled him a “white supremacist” and called Vice-President-Elect Mike Pence “one of the most anti-gay humans in this country.”