The example you give is not a correct use of this expression. 'To differ' - in this sense - is a rather formal type of word, meaning to have a different opinion from another person. It is mainly used in two set phrases 'I beg to differ' and 'Let's agree to differ'. In the example you give above, the correct phrase should be: We'll never agree, that's clear. So let's AGREE to differ. The meaning is clear from the context, as the sentence effectively explains the expression. 'I beg to differ' is a rather pretentious-sounding way of saying 'I don't agree with you'.

to beg to differ = to disagree with something It is a formal, polite way of disagreeing without sounding too harsh or blunt.