You can marry a cat in a pretend marriage ceremony but it won’t be a legal marriage. There is nothing stopping anybody going through a marriage ceremony with their cat but it would be without a proper, appointed person conducting the ceremony and it would not be a binding marriage in the eyes of the law. However, it might please the cat’s owner.
I think that you will find that anywhere on the planet the above situation applies. Wikipedia refers to a marriage between a man and a cow in Bali which took place after the man has sex with the cow! It appears to have been a one-off marriage ceremony which uniquely took place in order to cleanse the village of the immoral act of bestiality.
The act of marriage is by definition between two people. Marriage is a human construct, it was created by humans for humans. On a moral level a marriage between a cat and a human wouldn’t work either because you wouldn’t have the consent of the cat! You obviously need the informed consent of both parties to the marriage. Cats don’t understand marriage. Some humans don’t either. And there’s a need to sign the register! Cats don’t have thumbs and therefore they can’t hold a pen and therefore they can’t sign 😉 .
What else can I think of which makes a marriage between a cat and a person impossible?
P.S. I can think of only one area where cats acquire rights under laws relating to humans where their rights are similar to those of humans. Cats can be the beneficiaries of assets and money under a person’s Will. However the terms are carried out by a person, the cat’s guardian/caretaker.