A simple challenge for atheists

[Esquilax]

So we are left with if a hypothetical "miracluous" event occurs then we know:

1. Its cause is not natural
2. It may be a supernatural random event (no purpose)
3. It may be a supernatural directed event (purpose)

I'd be even more careful than that, as a non-natural cause doesn't necessarily mean a supernatural one either. I'd be looking for evidence of supernatural causation, not just the absence of a natural one; making assumptions based on a lack of data rarely produces accurate results, and when it does, it's purely accidental.

If purpose is evident in a supernatural event, why can't we conclude a purposeful supernatural being?

You could conclude that, sure. But I'd add that "supernatural being" also doesn't necessarily mean god, for the same reasons that a lack of natural causes does not entail supernatural ones.

There is no logical reason to say that a supernatural event can't be witnessed. What makes it different than any other event witnessed. The witnesses use the same sense data. It is not logical that the event itself has the power to make sense data unreliable.

Events in general can be witnessed; I have no issue with supernatural ones being witnessed either. But merely witnessing an event doesn't testify to its cause; that requires additional investigation, and so far we've only ever been talking in the abstract, rather than about specific examples, so we haven't established supernatural causation for anything.

See, this is why we doubt eyewitness testimony, as it is necessarily limited by the understanding and perceptions of the witness themselves. When we're talking about the gospel authors, inhabiting as they did a pre-scientific time period with an incredibly limited understanding of the natural world (I'd remind you that the bible is the same set of books that label rainbows as miracles from god) then their testimony is shaky at best; frankly, their go to response to anything they didn't immediately understand was supernatural, even if we take their testimony as totally real, eyewitness testimony... which we have no reason to do. All we could say, at best, is that the gospel authors believed they saw some supernatural things.

That's hardly surprising. It was a common conclusion to come to, back then.

Why isn't "Extraordinary claims require extraordinary evidence" special pleading?

Because it isn't; it's not demanding special consideration or exemption from consideration for a given concept without justification, it's demanding appropriate consideration given the nature of the claim. It utilizes exactly the same scale of required evidence that every reasonable person uses; the claim that one hundred people were murdered at once requires more evidence than the claim that one person was murdered. That's not special pleading, it's the nature of the investigative process.