Dude, you’re not paying attention. Nobody says that the unfalsifiable nature of the soul is evidence that it does exist. Rather, it’s the inadequacies of the material explanation which provide support for the non-material one.
Besides, why should we reject a hypothesis becuase it’s “unfalsifiable”? That’s a ridiculous reason to reject it! (Before you object, your exact words were “we can’t use the unfalsifiable nature of the soul as evidence that it might exist, since under my philosophy that is a reason to reject it.” No backing out of that statement, fella.)
One might reject a hypothesis for other reasons – inconsistency, for example – but it’s absurd to reject something because it can’t be falsified. A falsifiable statement is less reliable than an unfalsifiable one.
Maybe you meant “untestable,” dude. That’s still a lame reason to reject something though. Non-scientific matters, such as philosophy, are usually not testable in any strict sense. (Heck, even scientific matters aren’t always testable in a rigorous way.) It’s kinda lame to demand testability for philosophical issues such as whether man is 100% part of nature.