Guru Pathik wasn't wrong. He was just teaching the wrong version of detachment for Aang.
Detachment works for a monk whose only responsibility is their own soul. The Avatar's responsibility is the entire world. You cannot protect what you don't love.
Yangchen told Aang this directly, the standard monk philosophy doesn't fully apply to the Avatar because the Avatar can never fully detach from the world. That's his job.
What Aang had to release wasn't Katara. It was his need to control what happened to her. The fear of loss was the block, love never was.
Katara's voice pulled him back from blind rage in the Avatar State more than once. His attachment didn't destabilize his power. It anchored it.