Those are both examples of fallacies committed by Christians and atheists alike, and also agnostics. In fact, it's committed by everyone.
I believe the first fallacy is called appeal to certainty, claiming that if something can't be 100% proven, it's not true.
The second fallacy is called the burden of proof fallacy. That's like saying that you can't disprove that there's a teapot floating in space and therefore the said teapot is floating in space.
It makes someone look very inconsistent when they commit both fallacies.
Ironically, though, this meme seems to be committing the fallacy fallacy, which is the fallacy that claims using a fallacy in an argument automatically makes the claim false. That wasn't explicitly stated, so I could very well be wrong about that.
Caption this Meme
