If you want someone to accept a claim, you should be providing proof of some sort. That doesn't necessarily lead to a requirement to justify a claim however. I gain and lose nothing based on whether a claim I make is accepted or rejected by others.
The situation gets even more complicated when you start trying to determine what is acceptable proof. By and large, this is where the scientific method comes in, it tries to define a process to ensure evidence is useful, repeatable and transferable. This does not make the process a defininer of reality though.
To add to this, you must remember that any counter-claim (such as God doesn't exist) also had the burden of proof. In most debates, each speaker generally has their own burden.