Of course you can't ignore details. I was explaining the source of emotions, which tend to drive whether one wants to adopt a particular tool or method.

That being said, I often find convincing, false proofs as illuminating as true proofs, once the flaw is clear, because they highlight the nature of the conjecture. So I disagree with your claim that a proof can suddenly become useless due to a slight misstep.

And for what it's worth, theorems are rarely thrown out due to pathological corner cases; at least I've never heard of this happening. Instead, if the insight conveyed by the proof is useful, it's called a partial result and the conditions are modified to fit the proof. Entire theories are built up specifically to avoid pathology (almost every mathematical field does this)