"JerryZ:
The priest has the authority to set the pennance!
Let say I steal money and go to my priest and confess the sin and my priest says OK I will absolve you but you need to pray this and that AND return the money I stole.
In order for my absolution to be valid I have to comply with all the requirements, otherwise I am NOT absolved.
Perhaps you meant a different word than “agree?”

Penitents do not “agree” to a penance. There’s no negotiation or invitation involved. It’s simply assigned, according to the discretion of the priest.
Actually, I was very deliberate in my choice of words! I thought the same thing that you did, and was quite surprised to learn that I was in error! From the Rite of Penance (#18):
[T]he priest imposes an act of penance or satisfaction on the penitent; this should serve not only to make up for the past but also to help him to begin a new life and provide him with an antidote to weakness.
So, the confessor
does have the authority to assign a penance. Does this imply that this authority is to be unilaterally exercised, without (name removed by moderator)ut from the penitent? No (cf Rite of Penance, #44):
The priest proposes an act of penance
Note that it doesn’t say that the priest simply says “this is it” and the penitent has no recourse; rather, the priest merely
proposes; if the penitent is unable to do the penance (our case here, if the confessor said “expose your sin to public scrutiny” is an extreme case; another might be the case of a person who stole a car, and the confessor proposes “ok – leave $15,000 at the doorstep of the car dealership”, and the penitent replies “I can’t! I don’t have $15,000!”), then it is legitimate to object to the proposal.
Of course, that doesn’t mean that the confessor gets one chance at a proposal and the penitent is off the hook if he says ‘no’:
The priest proposes an act of penance which the penitent accepts to make satisfaction for sin and to amend his life.
So, there must be an
accepted penance.
I would suggest that we are so used to being told “say prayers A, B, C” or “do X, Y, Z” and we say ‘ok’, that we’re unaware that this is a
dialogue and not a
command…
The penance is the outward sign of the penitent’s contrition, but is not “essential” to the rite. For example, on one or two occasions in the last several years, I have forgotten the specific penance the priest gave me. I assure you that forgetting what it was, and even forgetting to complete it, did not invalidate my confession in the slightest.
Absolutely – forgetting a penance is not equivalent to saying “I refuse to do this”; the former still implies contrition, while the latter seems to imply a lack of contrition (in the unwillingness to make satisfaction)…