Hi Marion,
I see both sides of this issue....and you are both right and both wrong. There's no club steadfast rule stating you have to inform the club you are leaving....however, on the other hand, it would be courteous and polite to let the club know of your intentions so they can fill that slot on a more timely basis.
Maybe in the future, when someone joins, besides all the other information, you might also make them aware to please inform the club should they ever feel the need to leave for whatever reason they choose. Actually you might want to also enlighten all current members of the same....just saying!.