Why do you have to turn the VCR off when you program it to record?

Answer 1

Questionable user interface design on the part of the makers of the VCR.

They seem to assume that if you are actively watching a channel on the VCR, you don't want the VCR to interrupt you and switch to a different channel. If the VCR is turned off, it is a good assumption that you are not actively watching TV using the VCR and so it is okay to switch the channel.

VCR makers could have displayed a small message asking if it was okay to switch the channel or just switch the channel if the user doesn't click a button on the remote control, just as TiVo does.