I was in college when I got obsessed by "Logic". I was in my Ayn Rand avatar and thought logic is the ultimate tool a man has. Just think logically and everything falls in place, since then I have lost some faith in Logic.
Logic is a mode of reasoning and really, if you think about it, is there any other way to think but logically? Any sort of thought process is a logical thing; it is impossible to think illogically. The problem is that using logic is not an absolute and will not lead you to a generally accepted "truth". If there was one logical process of inferring by reasoning, everyone in the world would all arrive at the same answer. Everyone looking at the same set of data would "logically" come to the same conclusion. But that is not the case.
An example of where logic tends to cause a big problem is science. One would think doing a set of controlled experiments and obtaining a set of results should be *relatively* straightforward. Yet, the problem arises when interpreting these results by using logic. One scientist uses what he seems to be a logical explanation for the phenomenon, whereas another scientist's logic leads him to another completely different answer.
Science is just one example of this issue with using logic. You can try this experiment on various subjects - try to apply logic coming from the mindset of various different value systems. You'll find that you have arrived at various results. One mind applying the same "logical" process will get various results depending on how the subject has been approached. Therefore, every person thinking logically produces millions of ideas for the same few concepts. This is what makes the world as we know it. There is no way to know how it would be if we didn't think logically. The same occurs with religion and philosophy - a written word is interpreted millions of different ways. This, in turn, means each individual will not necessarily believe in the same set of tenets although they may be reading the same exact scriptures.
We need to realize that logic is not what it is advertised, it is a tool to reach a conclusion, yes, but not the same conclusion or a correct conclusion (whatever that means). In fact, it will make you reach where you already knew you wanted to go! So why go through the stress of doing this exhaustive logical exercise? The only reason is, by applying what you believe to be logic; you can justify and feel good about your own belief. If you really think about it, most of the time you already know which side you belong to and what you want. But the need to be a scientifically (pseudo) intelligent person, you have to push it through the bureaucracy of logic in your brain.
So why use logic? I guess probably because there is no other way to form our thoughts or take action but by internalizing it in brain. So relax, and take it with a grain of salt. Next time you are in a discussion, and you see someone seriously, logically breaking the concepts down and are frustrated that you don't get it; it is because both sides have taken a different tunnel and are deconstructing the idea differently and expecting to meet at the same point. Each expects they are right because they both think they are putting logic to test, but the problem is that logic is not absolute. It is a tool, like a shovel, that lets you dig and reach wherever you want.
Humans are stuck in a very contradictory body. Speaking in poetic terms, the heart and brain don't tend to agree. The mind is to blame - although physics may be bound by certain laws, the universe is really not. It is prerogative of Physics to explain Universe to be bound by laws of physics, not vice versa. In the same manner it is Mind which needs to explain things in a logical way but the life around you is not bound by it. When it comes to the human experience, our universe is not one bound by logic. Only our mind is bound by it. The world goes on illogically, without rhyme or reason, but our mind has a compulsion of trying to explain it logically.
An attempt to explain things which are illogical, by applying logic to it, is one of the fundamental mistakes of the human brain. This mistake also leads to unhappiness and misery.
My point is - Realize the limitations of your mind's logical thinking and understand the illogical nature of life around. Really, logic is just a tool for the illogic to rule.