Translation:Even though I prefer cats, my wife wants a dog.
Word order is very important in English. "I like cats more" is not the same as "I like more cats".
"I like cats more" = "I prefer cats". For example: I like dogs, but I like cats more.
"I like more cats" = "I would like to have more cats". For example: I have two cats, but I would like to have five.