Objection 1. It would seem that a man ought to have contrition for another's sin. For one should not ask forgiveness for a sin unless one is contrite for it. Now forgiveness is asked for another's sin in Psalm 18:13: "From those of others spare thy servant." Therefore a man ought to be contrite for another's sins.
Objection 2. Further, man is bound, ought of charity, to love his neighbor as himself. Now, through love of himself, he both grieves for his ills, and desires good things. Therefore, since we are bound to desire the goods of grace for our neighbor, as for ourselves, it seems that we ought to grieve for his sins, even as for our own. But contrition is nothing else than sorrow for sins. Therefore man should be contrite for the sins of others.
On the contrary, Contrition is an act of the virtue of penance. But no one repents save for what he has done himself. Therefore no one is contrite for others' sins.
I answer that, The same thing is crushed [conteritur] which hitherto was hard and whole. Hence contrition for sin must needs be in the same subject in which the hardness of sin was hitherto: so that there is no contrition for the sins of others.
Reply to Objection 1. The prophet prays to be spared from the sins of others, in so far as, through fellowship with sinners, a man contracts a stain by consenting to their sins: thus it is written (Psalm 17:27): "With the perverse thou wilt be perverted."
Reply to Objection 2. We ought to grieve for the sins of others, but not to have contrition for them, because not all sorrow for past sins is contrition, as is evident for what has been said already.
Source: Summa Theologica (New Advent)