If you are engaged in some form of argument or debate and it's not going anywhere, you can either refute their most recent points or ask that they stop arguing with you. If you refute their latest points and ask that they stop arguing, you are trying to get the last word in in a spectacularly annoying way. If you really think the argument isn't going anywhere, say that and that you think you should stop debating it. It doesn't mean you think they're right; it just means the debate should stop. But you don't get to say, we should stop and you should hear more of my side. If the argument isn't going anywhere stop trying to make it go.
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