In that particular case it was a chartered flight in a corporate type aircraft. He was paying a lot of money to go somewhere.
And I guess that following your arrogance he never used your company again.
10 out of 10, gold star and no tick.
When it comes to arrogant posters SNS3, you have the patent!
Tell what the solution is: you go and explain, quietly and calmly( borrowed from arrogant poster who knows better than anyone else - but he's probably "Murcain", redneck and proud of it) , that you can't carry him on the boarding card he is holding as you aren't permitted to, either by your airline, the CAA or the DFT.
You explain to him that his refusal to get off when asked is not helping the situation and that if he will accompany you to the gate you
MAY be able to check him in, even though check in has technically closed, however, you can't guarantee anything, but will do your best.
If it doesn't work out, you will have to leave to him behind.
Fortunately, you manage to get him checked in and get a boarding card issued for the flight and make your slot.
On arrival the pax asks to visit the flightdeck, shakes your hand and offers his heartfelt thanks.
Arrogant my dear SNS3? Not at all.
I do my best on the basis that I would like to be treated the same way but get ticked off when loudmouth know it alls think they have a licence to complain about flight and cabin crew because they fly a freighter, or worse, have a PC with flight sim.