The wider the variety of arguments against a specific assertion, the more likely the assertion is to be false.
When something is false, there are always going to be multiple angles and perspectives from which the falsehood can be perceived and exposed. So, a false claim is always going to have more observable flaws than a true claim, and many of the arguments against it, however weak or relatively unconvincing they may be, will be correct.
Compare the vast panoply of arguments against evolution to the relatively narrow range of arguments against the existence of God. While I personally don’t find some of the Intelligent Design arguments against the theory of evolution by natural selection to be particularly convincing, they are logical and they are also, in the end, absolutely correct. I happen to find appeals to conclusive mathematical analyses considerably more convincing myself, but it’s important to keep in mind that these various arguments are all ultimately correct because they point to the truth: what could not happen did not happen.
Now consider the various arguments against the existence of God. They are not only inconclusive, but they all amount to different flavors of the same argument: the appeal to personal ignorance and incredulity. The few attempts to utilize reason and logic are feeble and false even when they are not provably dishonest. See: Euthypro.
Anyhow, I think it’s possible that my philosophical Razor may be a more reliable heuristic than that of William of Ockham, which relies upon parsimony, and, in common use, is usually misapplied to competing hypotheses with varying explanatory power.
When presented with competing hypotheses about the same prediction and both hypotheses have equal explanatory power, one should prefer the hypothesis that requires the fewest assumptions.