Asking B

I would delete "one-side" from this sentence and add the word "don't".  The way to make a convincing argument is to support one's claim with evidence or facts.  One person's position in an argument is always only one side. A mediator might show both sides of an argument, but since you are talking about someone who is making a claim I believe that it should be expected to be one-sided.  I would change "unconvincing" to "less than convincing" or "will not be convincing". 

Your argument will be less than convincing if all you do is make a claim and don't support it.