I suspect this is silly, but I think I figured out why I am so annoyed with Zutara.
I won't bat an eyelash to Katara/Toph, Katara/Mai, Katara/Haru, Katara/Ty Lee. the list goes on. I don't mind Zuko with anyone but Katara. And at first I was unsure; because I don't adore Kataang as is. I'm a fan of future development. I love Maiko, but seriously, Mai with anyone pleases me.
I realized I didn't like Zutara because Aang loses two people he loves and two people he trusts the most. Katara leaving Aang for someone other than Zuko is all right; because Zuko's there. Zuko becoming cold to Aang over the years is all right, because Katara is there.