Gods just don't seem to fit in anywhere...no evidence or explanatory power.
A couple points: (I) the theist will obviously disagree that there is no evidence for God's existence; (II) Even if there was "no evidence" for God's existence, it would be fallacious to then conclude that God does not exist. You seem to be aware of this, however, given your previous comments on the matter. To illustrate how such an inference would be fallacious, consider the following syllogism:
P1.) We have no evidence of extra-terrestrial life.
C: Therefore, no extra-terrestrial life exists.
This demonstrates how the inference:
P1.) We have no evidence of God's existence.
C: Therefore, God does not exist.
is fallacious.
(III) the theist does not argue that God exists because his existence offers explanatory power. That would just be tantamount to a "God of the gaps" defense which no academic theistic philosopher defends (indeed, you'll only find theists expounding some "God of the gaps" argument on some internet bastions of ingorance, e.g. YouTube). Theistic arguments rather typically involve some observation, be it
a priori or
a posteriori and then work from there, to put it simply, to the conclusion that God exists, e.g. Aquinas' "there is change" or Craig's "whatever begins to exist has a cause", etc.
But of course, tis impossible to disprove their existence, so I'm "weak".
Again, it is not impossible to prove that God does not exist. In order to do so, one would have to argue that the concept of God is itself incoherent, as the concept of a square-circle of a married bachelor is incoherent, for example. Many atheistic philosophers have some interesting arguments that purport to show, for example, that God's omniscience entails some contradiction or other and so that God cannot exist. Even if such argument ends up being unsound, such atheist is actually attempting to provide a good reason for his atheism, rather than simply sitting and uttering fallacious armchair nonsense to the effect of "there is no evidence for God, therefore he doesn't exist lol".