There is one dynamic in which I resist logic: It is when much relevant information has to be discarded in order for the logical approach to work. It is convenient to use logic when all the data that goes into the problem can be defined, measured and known. Very few aspects of life can be reduced to a logical syllogism without dismissing a great deal of the true complexity of the situation, without relying on generalizations. Consequences in the world result from so many different sources, so while I can agree with a specific series of logical cause-and-effect, I can also notice that it doesn't address the entire system. Many of the ideologies of the 20th century had quite solid logical underpinnings and yet the application caused great misery, unforeseen consequences, and failure.
Logic is often used in this over-simplified manner and becomes much like aspects of modern medicine that looks at the fix of one isolated organ or symptom without looking at the entire system. That approach to 'logic' is what rules so much of our world. The corporation must make money for the stockholder and can create A-B to make that happen without examining the effects on the larger systems in the world. That immature, careless use of logic is tiresome because, yes, the isolated logic can be correct, but within the larger context can be wrong and have unforeseen effects.
Try to convince an ego invested T with logic and you can see the results demonstrated across so many forums online. It's extremely rare I've ever seen a T convince another T of anything online *using logic*. It can certainly happen, but the reality is that ego is a far greater obstacle to reason than the cognitive processing of an F.