I don't understand your objection. Did you have bad hunches? Did you check that your bad hunches were actually meaningless?
If you failed at becoming a mathematician because you have usually bad hunches, why should you be included as a counterexample to a claim that mathematicians have usually good hunches? P=>Q is fully compatible with (not-P AND not-Q).
If you failed at becoming a mathematician because you have usually bad hunches, why should you be included as a counterexample to a claim that mathematicians have usually good hunches? P=>Q is fully compatible with (not-P AND not-Q).