People believe in the super natural because they see evidence in the natural world that points toward the super natural. These would be the existence of a finite, dependent universe subject to the law of causality; The existence of a moral standard that is ingrained in all human beings, that causes us to view things as 'evil' and 'righteous', and many other things that demand the super natural for their explanation. If these arguments can be refuted then
in a way belief in the supernatural is falsifiable and thus potentially true.
I say it can be 'in a way' falsified, because some of us have encountered God. That cannot be falsified. Therefor even if scientists and philosophers could deal with arguments for the existence of the super natural, we would remain convinced 'super naturalists'.
Also I think that the falsification principle is applied wrong since it was only meant to deal with empirical questions and not metaphysical questions. There are many things that are meaningful that cannot be falsified, such as the statement, "Only statements that are falsifiable can be meaningful". Is that a falsifiable statement?
This type of argument stems from logical positivism, which says that only that which can be verified with the senses can be meaningful or true. But that statement itself cannot be verified with the senses, and therefor is false. So while they are claiming 'empiricism', the core tenets of this empiricism are not 'empirical', in other words, they have non falsifiable beliefs that lead them to the place that says non falsifiable beliefs are rubbish. A bit inconsistent.
We have some philosophy buffs lurking here on the board(hem hem Christian Trader) who would be able to refute logical positivism and answer this question much better then I did, but I hope this helps some.