I don't want to babysit my uncle's dog
Do you not like your uncle much?
No, it's just I don't like dogs.
Dogs are great pets but you don't have to take care of them if you don't like them. They are a big responsibility and not for everybody. As long as you explain it to your uncle, he should understand.
My uncle is such a jerk. If I liked dogs then I would feel bad for his.
If you just tell him you don't feel comfortable taking care of dogs then I'm sure he can find someone else to do it.