As we saw yesterday (see here) to be God's chosen people is not about having more rights, but more obligations. After all we, the Jewish people, are the single witnesses of God's existence (see Yesha'ayahu 43:10). In Shabu'ot God revealed His existence to us, at the time He pronounced the Ten Commandments. The case for God's existence does not rest upon evidences--scientific or philosophical--but upon our testimony.
In one of his letters (Igeret Teman) Maimonides explains that the first thing a Jewish parent should teach his child is what happened in Shabu'ot. When we witnessed God's revelation standing at the feet of Mt. Sinai. And by our testimony we turn our children themselves into new witnesses of God's existence.
A Jew is a living testimony of God's existence. The worst offense in Judaism is Chilul HaShem, desecration of God. It happens when a Jew--one of God's witnesses--misbehaves in a public context. When a Jew makes a personal religious mistake it is a private matter to be resolved (and hopefully absolved) between him and God. But when a member of the Jewish people acts inappropriately in public or when his moral misbehavior becomes public knowledge, then his act is considered Chilul HaShem, a desecration of the name of God.
Why?
In a court of law a witness could be disqualified for a questionable immoral conduct. Some unethical acts will affect the credibility of the witness and his or her testimony will be inadmissible.
If a Jew acts with dishonesty, cheats, misbehaves, etc. then his character as a witness is affected and his testimony is invalid. It is a desecration of the name of God because a disqualified witness for the case of God, weakens the case for God.
Being a Jew is a tremendous responsibility. It implies to know that we have to live and act as credible witness of HaShem.