I wish to describe an explanation, which is broadly correct, but which glosses over some potentially important details.
The nearest term I can think of is "hand-waving explanation". Is there something more formal I could use instead?
Learn English – more formal term for a “hand-waving explanation”
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Though not familiar with your "hand-waving explanation," I think I know where you're going with this. There are any number of possibilities:
On the face of it . . .. (In other words, the explanation sounds good initially, but given a closer look, maybe "not so much!")
A prima facie explanation (Again, an explanation which upon closer inspection may have some flaws. It satisfies certain conditions but not necessarily all.)
An ill-considered explanation
A rush to judgment (This is an explanation for, say, the guilt of someone, before all the facts have been gathered, inspected, and verified.)
An interim explanation
An unsubstantiated explanation
An incomplete, inadequate, superficial, surface, incomplete, or partial explanation
An ostensible explanation, but upon closer examination . . ..
A cursory explanation
An explanation which at first blush seems adequate, but upon closer examination . . ..
An unthought out explanation
An ad hoc explanation
These should at least get you started, I hope!