Shabbos 54 – שבת נד

The Gemara discusses kilayim when a person and animal perform a join task.  Tosfos says this is referring to owner who is pulling the rope (of the reigns) together with the animal.  Since the rope is ‘batel’ to the animal and is not considered a load (even for the owner holding on to it) with regards to Shabbos, why is it considered carrying when it comes to kilayim?