Beg to differ literally means we beg your pardon; we want to express a different opinion. If you understand “beg” only in the sense of “First you borrow, then you beg”, I can understand the confusion.

Beg to differ literally means we beg your pardon; we want to express a different opinion. If you understand “beg” only in the sense of “First you borrow, then you beg”, I can understand the confusion.