The person you’re talking to is unlikely to be pursuaded but there’s usually silent, invisible lurkers who can be.
I know I’ve changed my mind on things because of arguments I’ve read on the internet.
It is proven that people do double down on their views when confronted with opposing evidence, but IMO this is more about the psychology of trust and confrontation between individuals, rather than proof of the futility of argument as a concept. Hell, Vsauce made a video called ‘The Future of Reasoning’, where he makes the case that argument might have been selected for as an essential part of human psychology and necessary for our survivial.