Cliquez pour agrandir I think "Brian rejects [what I said, propose, am offering] out of hand" might be a good idiomatic English translation, if I understand the nuance of the French term correctly.
As far as I can surmise, "une fin de non recevoir," in the everyday sense, is a site de rencontre wordreference or refusal of a claim without even taking the specifics of the claim into consideration.
For example, if site de rencontre wordreference customer in a restaurant smacked their server across the face because there was a hair in their soup, and then requested a refund for the hair in the soup, their request might be rejected out of hand, because they reacted in an inappropriate manner to the situation, which thereby disqualifies their request from serious consideration.
I think in that case you could say that the restaurant owner "oppose une fin de non recevoir" to the customer when they come back the next day asking for a refund, after being chased out for being violent the day before. Is this correct? I'm kind of trying to help, but at the same time trying to see if I understand the French expression myself.