Finnish is generally gender neutral anyway, apart from words like fireman etc. but it's also funny to me that you won't necessarily know if someone is talking about a single entity that is a human, a plant, a cow, a dog... But you'll almost invariably know when it's a cat!
Anyway. The whole "hÀn" pronoun is apparently a clerical invention because religious people wanted god to be referred to with a more fancy word than any old people. And Finns immediately went: Ah yes, use this word for cats and/or deeply sarcastically, then!