"since it contains a fallacy, its conclusion must be false" Actually, this is not quite true in this case. I pointed out the fallacy but also the fact he uses

"since it contains a fallacy, its conclusion must be false" Actually, this is not quite true in this case. I pointed out the fallacy but also the fact he uses no argument / data to prove his point. I made no such claim that his statement is false (or because of the fallacy is false).