We are taught at every level of Jewish education to be proud of our level of religiousness. In a world where so many people are not Jewish, and so many Jews are not religious, we see ourselves as the sole representatives of God. This message is good and necessary because without it, it would be much harder to motivate ourselves in sometimes hostile surroundings.
However, at one time of year - during selichot - we need the opposite message. The main theme of selichot is that we are utterly worthless. We begin with a long list of praises of God's greatness, and we are insignificant in comparison. We ask for mercy not because we have any legitimate claim to mercy, but only because of promises to the Avot, Moshe, and appeals to God's honor.
It is like someone asking for a job, who admits they are incompetent, but wants the salary anyway in return for a favor his relative once did for the employer. Anyone would be embarrassed to ask in such a manner. We too should be embarrassed to approach God this way, but we have no alternative.
(Summarized from a shiur by R' Ezra Bick, 9/16/2006)