The 5 Branches of Philosophy
Life As the Moral Standard
Reason Is Man's Means of Survival
Harmony Of Interests
Integrity is the virtue of practicing what one preaches. Or more importantly, practicing what one believes is right. A 'man of principle' is not a man who understands a principle, but a man who understands, accepts, and lives by a principle. There are many reasons why integrity is a virtue.
The first and most important reason to practice one's beliefs is that if they are right, you will be benefiting your own life. To understand other virtues or principles, and not act by them, is destructive. It is an act against your own best interest. Any deviation from what you know to be right is an attack on your own life.
The second reason to practice integrity is that it is an affirmation that your ideas benefit your life. To act contrary to your own knowledge is accepting the premise that morality is somehow different from you own self interest, and that bypassing morality will somehow make your life better. Instead of seeing morality as a tool for survival, you see it as a restriction that make life more difficult. Every act that violates your integrity weakens the moral habit, until your emotions are unaligned with your thoughts. Further, it is an attack on the efficacy of one's mind. To act against your own ideas is to claim your own incompetence, or to claim the general inadequacy of reason to guide your life. Since reason is your means of survival, you will be abandoning your life.
A third reason to practice integrity is in dealing with others. A man who practices what he preaches is predictable, and few will feel threatened by it. Trust can develop, since others will come to realize you are consistently virtuous. To act without integrity, even occasionally, will leave others distrustful. This can negatively impact one's life in a number of ways. People won't allow themselves to become emotionally close to you. They won't trust that you'll pay back debts. They'll always fear your betrayal.