avahi-daemon disabled but is still started

I've run systemctl to disable avahi-daemon.service and avahi-daemon.socket. And yet, they both are running! I suspect that cupsd is responsible, but I don't know how to prove it:
Quote:

avahi-daemon.socket - Avahi mDNS/DNS-SD Stack Activation Socket Loaded: loaded (/lib/systemd/system/avahi-daemon.socket; disabled; vendor preset: enabled) Active: active (running) since Thu 2021-05-06 13:18:56 EDT; 5min ago Triggers: avahi-daemon.service avahi-daemon.service - Avahi mDNS/DNS-SD Stack Loaded: loaded (/lib/systemd/system/avahi-daemon.service; disabled; vendor preset: enabled) Active: active (running) since Thu 2021-05-06 13:18:57 EDT; 2min 44s ago TriggeredBy: avahi-daemon.socket

What can I do to prevent these progs from running. I need cupsd for printing.