Why do I have to deauthorize all computers if I just want to deauthorize an o-o-c MacBook?

Bought a new MacAir recently (MacBook Pro screen failed) and trying to clean up my Apple Music. Says 4 computers are authorized to play music but won't show me the details. Apple advice is to deauthorize all and then go onto each one and re-authorize? Seems stupid - why can't I log into my account and simply de-authoprize the old one?