Monkey surgery

We were playing with all our "friends" this afternoon when I noticed monkey had a cute Barbie bandaid on his tummy. I tried to take it off but noticed it was not coming off without a fight. I decided to go get some tweezers to see if that helped. They did but pulled off tiny pieces at a time. 30 minutes later I had successfully removed the bandaid. My question is why do the fall off skin but stick to fur like glue? A note to the wise... Never put a bandaid on your furry friends.