子 isn't pronounced as "nezumi". It could just means a mouse and with this meaning it is read as "ne". Ancient Chinese people divided the sky into 12 parts record time, and named them 子, 丑, 寅, 卯, 辰, 巳, 午, 未, 申, 酉, 戌, and 亥 respectively. Chinese people also combined each of them with animals. 子 is combined with a mouse.