Are people having two different discussions here.

Miracle = something unbelievably extraordinary.

or

Miracle = there's an external, (possibly intelligent) entity that can suspend the laws of nature, ie perform magic.

They're arguably the same thing. I suspect that it's just that some people have a wee bit too high trust in their faculties and draw the conclusion, "I don't get it, therefore it is magic".

I wouldn't be surprised if the border between these two interpretations simply comes down to what level of education you've passed.

I believe in miracles to. But I don't see any shame in not understanding everything.