The problem with shifting the burden of proof is that you're supposed to be doing more than just making a claim. You are supposed to be defending a claim. You can never commit a fallacy by stating a belief; fallacies only occur when you are tying to convince another person that your claim is correct.
If you make a claim, but do not provide any evidence to back it up, then there is no reason for anyone to change their minds. They may happen to agree with you, but you should not expect them to.
If you introduce a viewpoint into a debate and then cannot back it up, this is a bit annoying to the others you are speaking to. If you spend any time insisting that you are right and the others are wrong, you are just being rude*. In philosophy, we call rudeness a fallacy (we have to discourage it somehow).
There are plenty of times when an statement doesn't need to be proven; we might all state our religious beliefs, for example, without having to defend them. But when we start trying to convince others that they should follow our religion, we need to give then some sort of reason (some 'proof'). If you just state loudly that you are right and everyone else is wrong, you will be accused of being illogical, and asked to leave the debate -- and for good reason.
To apply Shifting the Burden of Proof to the religion example:
Person 1: You should believe in my God.
Person 2: Why?
Person 1: Do you have a good reason why you shouldn't believe in my God? (That was shifting the burden of proof).
Person 2: No -- do you have a good reason why I should? (and that was shifting it right back where it belongs).
Note that Person 2 still hasn't stated ier belief; e may or may not believe in Person 1's God. E may also belive in any of a hundred thousand other religions. The burden of proof lies on the one making the claim in this case because there is no other claim.
There may be other debates where there are a set number of possible conclusions; ideally, in these cases each conclusion will be argued for as strongly as possible. In these cases, shifting the burden of proof would prevent one of the options from being explored properly. (Again, blocking someone from looking at your argument and judging it fully is not conductive to a rational understanding of the issue {and it's rude}, and therefore, labeled a fallacy).
* Rude? Yep. You aren't going to trick anyone into thinking that you're right just because you're persistent. You are interrupting what (we hope is) a serious debate. You may not be wrong, but you are rude. And pointless.