It's about Rudy, in a fashion befitting a dictator, outlawing ferrets just because he doesn't like them.
That's the critical factor here.
Keeping ferrets as pets has been illegal in NYC since 1959 -- Rudy had nothing to do with the creation of this law. I really doubt Rudy cared much one way or the other whether ferrets were legalized, and was probably just backing the Health Department's position, on the grounds that they had the most knowledge of the matter, and little incentive to make extra work for themselves in enforcing the ferret ban if there wasn't a good reason for it. Given the level of discussion that reportedly went on in the city council (my rabbi says I can't vote to legalize them because they're not kosher, babies smell like rabbits and so ferrets might attack them, etc.), it's little wonder Giuliani preferred to back the Health Department's position.
Personally, I think the anti-ferret law is unnecessary, and that the Health Commissioner who Giuliani backed, was just being obstinate. But Giuliani's point was that the matter should be handled through the Health Department, which has the authority to change the classification of ferrets, and not by the City Council. If Giuliani sometimes seemed overly passionate about maintaining the ferret ban, I suspect it was because he was annoyed at the amount of time being spent on this trivial issue by levels of government which should have been busy with much higher priorities.
The City Council initiated a move to lift the ferret ban in 1999, when Giuliani was mayor, and I think he got it firmly fixed in his mind at that point, that this was a Health Department matter that the City Council shouldn't be wasting its time on, and he stuck with that position. His widely quoted remarks on his call-in radio program suggested that he was simply fed up with the whole thing, both the City Council's involvement and some of the screwball New Yorkers who seemed to be making a full-time job of being passionate pro-ferret activists:
Addressing caller David Guthartz, executive president of New York Ferrets' Rights Advocacy, Giuliani said: "There is something deranged about you ... this excessive concern with little weasels is a sickness ... you should go consult a psychologist or a psychiatrist with this excessive concern, how you are devoting your life to weasels. You need somebody to help you. There are people in this city and in this world that need a lot of help. Something has gone wrong with you."