The very real potential that your stallion, or the mare... can be hurt. Allowed loose, horses will too-often kick and bite upon first meeting. A valuable stallion is pretty vulnerable to a well placed kick, and owners of valuable mares don't like them scratched up from a chasing biting stallion. Many breeders will put breeding hobbles on the mare as a precaution.
You are so right - somebody mentions pasture breeding my mares and they won't ever see them. I was upset last year with the stud we took one of our mares too because she came home with bite marks on her neck. Excuse me - he might be a young stud but teach him some manners :)