You don't ALWAYS have to mute on chord changes, but the reason Chris gets you practicing that way to begin with is as he explains - it provides a much cleaner change and you don't get any chord overlap. He also overemphasises the mute in the early lessons so you can actually hear him muting and to get you into the habit of doing it - in later tutorials and with different tutors there's no emphasis on it so you don't "hear" it but alot of the time it will be there, just in that fraction of a beat where your fretting hand changes position.