Wilson had obtained the cat when his neighbour died and he didn't want the cat to be destroyed. However, the cat was diabetic and needed regular injections of feline insulin to keep it alive. As such, Wilson didn't have a lot of time for House.
Wilson being busy all the time made House suspicious, especially when he heard a patient of Wilson's mention the name "Sara". House thought it might be a new girlfriend, but Wilson shrugged it off as the rantings of a senile patient. This did not satisfy House and he started snooping around, eventually breaking into Wilson's trunk and finding syringes and some organic material. He first thought it might be drugs, but on closer inspection he found out it was catnip.
House confronted Wilson about his deception and then started trying to make Wilson think he was allergic to Sara so he would get rid of her. He was afraid Wilson would withdraw socially and repeat an earlier episode where he became attached to another pet who House had to let escape. House tried to take Wilson out for drinks, but he bombed out with an attractive barista he knew.
Finally, House gave in and started buying mice for Sara to chase around Wilson's condo.