Your statement is obviously your rationale. That's a start. It shows you have a mind, and that you are thinking. Good.
In the same rational way of thinking, consider this:
If I were tall and you were short and could not see what was on the top shelf, your statement "A winged rabbit and God are both “things” that can’t be proven." does not hold up.
You see...that is, you being short cannot see what is on the top shelf, proves rather that you cannot see what I who am taller can see. Granted, that reality does not prove anything of what is on the shelf out of your view.
So, back to your point of "unfalsifiable claims" serving "no purpose"--that's just wrong. If I (being tall enough) tell you what is on the top shelf that you cannot see because you are short, the purpose is to inform you. Now, under those circumstances the response of a "reasoning" person like yourself, should rather be to simply say, "I don't care." or "I wasn't asking." But that is not what you have done...which, to the contrary, does not make you the "reasoning" person you claim to be. On the other hand, offering missing information to someone who is without--is indeed reasonable, and kind, and giving, and a bunch of other good stuff.
But here you are pointing the finger. Why don't you actually try being reasonable? Now there's a good question!
But, hey, there is already an unanswered question on the table--the one you should have asked: "
What's on the top shelf?"
Want the answer?