per or kun
La kato ludas per la fadeno. The cat plays with the thread.
Why would one not say, "La kato ludas kun la fadeno"?
Because the cat and the thread are not play mates. The thread is something the cat use to play.
Think about the sentences:
Mi skribas per la skribilo
Mi skribas kun la skribilo.
In the first one I use the pen to write, in the second one the pen is with me while I'm writing but I'm not telling what I'm using to write.