No. The burden of proof is with you to demonstrate theism.
I think you misunderstand the issue here. "burden of proof" does not make any sense in this context. Burden of proof is not a principle we should always endorse. And if we endorse it in this cases, then it applies to both the atheist and the theist. Do you disagree with this, or anything I said in this regard, and if so, why? It's difficult to make progress if you simply repeat your claim, without engaging with the argument or claims.
I've never made that claim. Only you have. Please demonstrate how this is the case. OTOH, since this discussion is about theism, it's more salient to discuss that specifically.
It's unclear from your quote what parts of my explanation you want me to elaborate.
My particular world view isn't under discussion here. The burden of proof is on you to demonstrate theism.
I never said it was under discussion. I just started from what I assumed was uncontentious common ground. That's how arguments work. We work from mutually accepted premises. My point was just that since you accept theories which weren't falsifiable, it shouldn't be that surprising if theism wasn't falsifiable. This was in reply to you when you originally wrote:
Certainly, something as profoundly important as theism can offer both a verifiable and falsifiable hypothesis.
I fail to see why the profundity and importance of a theory has anything to do with verifiability and falsifiability. It rather has something to do with the structure of the theory. If I actually believe in a theory, and if that theory happens to be true, and if that theory isn't falsifiable, then something is wrong with the criterion of falsifiability, not with the theory.