Some of the most heated, seemingly-intractable arguments I've participated in have led me later upon reflection to change my mind. I'm thankful the other party didn't take this viewpoint that arguing is pointless.

Also, a just society needs to operate by certain fictions: for example, that people are innocent until proved guilty or that all men are created equal. Among those should be the assumption that others can be persuaded through logical means (as opposed to say force or habit). I think it's somewhat akin to the principle of charity.