There is a great deal of difference between a positive self-image and an arrogant one. Today's world places too much emphasis on this - to the point where we have men and women who do not have an adequate amount of self-deprecation in their personalities. We've raised a generation that feels better about itself more than any other - but this has not led to good things. Instead it has led to one of the most arrogant and foolish generations in American history.
When a man is "wise in his own eyes," he is conceited and arrogant. A man wise in his own eyes thinks he is a genius when he is not. He considers himself far too brilliant in his own estimation, which leads him to think far too highly of his own thoughts, ideas, and opinions. A wise man is one who learns to see things from God's perspective - not from his own fallen one. Since the fall of man into sin - and the ongoing choice in every generation to seemingly plumb new depths of that fall - wisdom is something that comes only as we learn to question our own fallen assumptions and turn to God and His Word for true wisdom. The more we do this, the wiser we become. But the opposite it true as well. The less we turn to God and choose instead to trust our own natural, fallen assumptions, the more foolish we become.
The man wise in his own eyes is fixed on himself and his own views and opinions. To turn him from them is not an easy task - some consider it almost impossible. He sees himself as the end-all, be-all of wisdom and understanding - and will argue with others about it until he is blue in the face. Considering all that God has to say about the fool - it is pretty amazing that God holds out more hope for the fool than for this man.
The admonition of Scripture on this is clear. Do not be wise in your own eyes. Fear the Lord and turn from evil. That is the counsel that God offers to us when it comes to the how we view ourselves and our own wisdom in life. To do otherwise is to mire ourselves in a pit of self-centered, foolish, and self-indulgent thought. The end of which is to so bury us under the weight of our own stupidity and selfishness that we cannot dig ourselves out.