My old man's work used to make them change their passwords once a month.

For the next 10 years, his password was a particular insulting phrase directed at the IT guys, followed by a number that would increment each time he had to change it. Got into the hundreds before he left the company.

I was doing the same at one point, albeit it only lasted 5 years before I changed employers. Didnt even had to rotate the numbers, I could always come up with new and colorful insults for the nameless IT group. Which ironically I remember perfectly.

I'm reasonably certain that I'm not your father but I used to do that too - although I don't think I made it into the hundreds.

I had a coworker that would type in something random as his new password, then immediately fail to login three times in a row so his account would get locked. To fix this the sysadmin would reset the password, and allow you to choose a new password... and on the no-repeated-passwords policy did not apply to the magical reset dialog. So he would then reset it to his old password.

Changing the password opens it to compromise when it's being changed. Capture of that account is possible and easy at that point.

It also interferes with password managers and secure keys. Opens a phishing vector. Generally I could enumerate how bad it is and run out of ink here. (And it's a screen.)