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If you can't be wrong in interesting ways, I can almost guarantee you that you can't be right for the right reasons.
Looping back to @Jonathan_Blow — you can't explain why you're right for the right reasons if you can't also explain why interesting counterarguments are wrong. And you'll inevitably forget all those "details" if you don't have a living, breathing model that can reconstruct them.
a famous example of this from mathematical history is the construction of non-euclidean geometry in an attempt to show that only euclidean geometry was logically consistent https://en.wikipedia.org/wiki/Non-Euclidean_geometry#Discovery_of_non-Euclidean_geometry …
specifically, Bolyai showed that nothing in logic constrains the physical universe from being non-euclidean (and it turns out it isn’t), through trying to find logical inconsistencies in “interesting but wrong” constructions of geometry
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