>A person who is not operating on logic, but instead trusts their emotions is going to be someone who will often be wrong where logic succeeds, but they will also be correct where it fails.

The definition of logic is "reasoning conducted or assessed according to strict principles of validity", which means according to the validity. From the term itself logic is impossible to fail in the search for truth and proper reasoning evaluation.

>A big example of this, and I'm sorry for this, is eugenics

Your example is illogical and invalid, and doesn't imply a fail in logic as a tool of derision making (a possible reason for this, could be the fact that you might act directly affected act by emotion). Through empirical knowledge it was proven how to change human characteristics wiyh the proccess of breeding. If we institutionalized using logical a system where "X" characteristics are better for "Y" reason, we can act n a possible way to accomplish it. If some people have a (meaningless) cynical negative emotional reaction to it and therefore such an act becomes social unaccepted and therefore doesn't be let to happen. Then is not a fail of logic but fail in a procedure cause by illogical acts, namely the absence of logic. The fact that X number of humans do not have a positive emotional approach to the idea of eugenics isn't a logical reason for it not to happen.