You handled it very well.
I call a situation like this "guest entitlement disorder". It can afflict anyone, even people whom under any other circumstance be considered nice.
Symptoms: When invited to an event of any type...wedding, dinner party, etc., an afflicted individual will make rude requests or demands of their host. They may also invite their own guest(s)--especially if not proper to do so, wear very inappropriate attire, and/or be the cause of any problems stemming from abuse of alcohol. In serious cases the guest may loudly state, "nobody's going to tell me what to do/how to live my life!" In a nutshell, the guest feels like they have a "right" to act however they feel, that they are entitled to such behavior.
Treatment: Refusal to cave in to demands, done tactfully but firmly. One common treatment is to give in to demands, out of a desire not to rock the boat. However, this treatment has limited success; in fact usually just makes the affliction worse.
Side note about the pet issue--I've had many guests to my home, and none has ever
asked that I put away my 135lb Great Dane. That said, I always put away my dog when I have guests, because not everyone likes dogs, especially huge ones (even though he loves everyone he meets). Even those that like dogs usually prefer the dog-free environment for an evening of entertainment.
Now I know some folks whose lack of tact can be shocking...they don't even seem to realize they're being that way. If that's the case with your invitee, perhaps what he was thinking was "I'd really like to go to this party, but she's got a cat? I know people who have cats and they walk all over me, the kitchen counters, the table, ick! I'll just tell her to lose the cat for the evening...no problemo"
Regardless, it was still rude, and you handled it quite well.
And as a side note...I really don't care for cats
Just because they wash themselves and have no odor does not mean they leave a home in the same condition. Any animal whose feet are touching floor surfaces or coming into contact with urine/feces have no business on eating surfaces. And I have yet to find a cat that can be kept off them. BUT...when invited to homes of cat owners, I certainly don't demand they lose the cat. Sounds like your friend should acknowledge that, or gracefully turn down the invitation.