In Beg to Differ?

: to politely disagree with someone You say that the candidates are essentially the same, but I beg to differ.

Is beg to differ rude?

"I beg to differ" is relatively formal, but not as formal as "I respectfully disagree" - this formality appears, as does a lot of formality in English, by virtue either of the old-fashioned "beg to" or the parenthetical "respectfully" that breaks from the normal word order and attracts attention to itself.

Why do we say I beg to differ?

The phrase belongs to the British region and is most popularly used in the same. ... The phrase is speculated to have been used by the Lords in England and the “begging” was as superficial as it could be. It was show of humility where none was required (or in some cases present).