People do not respond equally to reason and logic because they often do not see the mathematical equation that underlies all logic, or they are blinded by their own biases. Logic is nothing more than a system of reasoning that can be used to predict likely outcomes or ascertain likely causes. A logical argument is one that must be true or is likely true, given the facts. You have to agree to certain premises though, as a matter of faith. It is impossible to do without these premises without inconsistency and contradiction. One such premise is this: Whatever is, is. Something cannot both be and not be at the same point in time. These are premises that underly our system of epistemology. Without them, it is doubtful that we could agree to anything. Usually, most people will agree to them, but there are contrarians who will not, in spite of any and all utility and reason. Because they have no faith in reason, they have no reason. Because they have no reason, they have no faith (in the spiritual sense--they have faith that, for instance, of the unimportance of it all, but that's not what I'm talking about here).
So logical arguments should not be confused with contradiction. People who are in the midst of an argument often fall into this fallacy, whereas they should be looking for fallacies in the structure of the arguments or the premises of those arguments.