GIRM paragraph 51
"Before we get started I just want to apologize for any way in which I may have offended you."
That was easy enough to type, a lot more difficult to say in person. Employers and politicians are wary of apologizing. It might make them liable to a law suit because they have admitted to some fault.
For an individual to apologize is often difficult. It seems to place one at an instant disadvantage.
The Church is sometimes cautious about apologizing. It took a long time, in many cases, for the right people to apologize for the sexual scandal.
We have had three popes now that have done an awful lot of official apologizing for the corporate body of the Church. Granted, for many, no matter how much they apologize and attempt to change things, it will never be enough. On the other hand, the cleared air makes many more ears open. The strain and tension that closed ears off can open those ears and hearts once more to hear. I know that if someone at least acknowledges that I have been hurt in some way, I can then hear them better. It is a means of repairing relationships, opening pathways, clearing the air, calming troubled brows enough to make new progress.
So it is with us and God and the Mass. Before we enter into the big stuff, we take a moment to recall our sins.
"Brethren (brothers and sisters), let us acknowledge our sins, and so prepare ourselves to celebrate the sacred mysteries."
So, a couple of important things:
1. This is an opportunity to which you are invited. If someone chooses to think about the grocery list instead of their sins at the moment, he misses out.
2. If a person misses out, will he be fully disposed (healed, aware, open) to all of the graces available at the Mass?
3. And the inviter NEEDS TO GIVE PEOPLE TIME TO CALL TO MIND THEIR SINS IF HE IS GOING TO ASK THEM TO DO SO. In the General Instruction it calls for a brief pause for silence and in the place where the prayer is located it says again, "a brief pause for silence follows."
If we don't do these things, can we continue to believe they have any efficacy (even if the absolution that follows does not have the same efficacy as the sacrament of Penance.)
As side note, from time to time the Penitential Rite can be substituted with other things. One in particular mentioned in this paragraph is the blessing and sprinkling of holy water which reminds us of our baptism. This may be done "from time to time" and only on Sundays, but particularly in the Easter season.