BTW I'm a real vegetarian, not one of those people who call themselves vegetarians and eat fish??!!?!!
I'm an omnivore (and have gobbled up my fair share of piscine dinners), but I would agree that you can't call yourself a vegetarian and still eat fish/chicken/etc. That's just avoiding red meat, which many people do for health reasons.
What I do, sort of, understand is people who feel they're vegetarians and still eat eggs. That discussion has great potential to deteriorate into a political argument, however.
And back on the subject...I think the only reason why fish are still pretty much food, and cats pretty much aren't, comes down to the fact that we figured out an alternative use for cats much sooner. If we had figured out how to constantly lure mice into a big pit with an arowana in it, we might feel a little different about the scaly ones.