From the dictionary, forgiveness is: to give up resentment of or claim to requital for. b: to grant relief from payment of. 2: to cease to feel resentment against (an offender)
Penal substitution is essentially Jesus punished in everyone's place in order to satisfy God's justice. Through this process, humanity can receive forgiveness.
I suppose the first question that arises is this: is forgiveness truly forgiveness if the "pound of flesh" is measured out first? If someone kills your child, and so you kill that person's child in turn and say to the person that you now forgive him/her, have you truly forgiven that person? Or is the forgiveness based on punishment, and what is due to you as the wronged party?
For me, I tend to see forgiveness as not only releasing the negative emotions, but relinquishing any claim to compensation for the wrong act. Jesus mentions this a lot, in that one is to forgive, and not seek vengeance. If vengeance is sought, and then forgiveness is granted, forgiveness becomes dependent on satisfying the vengeance.
So does the Penal substitution theory, which dominates conservative Protestantism (and possibly branches of Catholicism?) violate forgiveness as it's commonly identified? After all, God doesn't forgive unconditionally. Someone still had to be punished before that forgiveness was granted to people. God didn't simply relinquish any claims of satisfaction -- those claims were fulfilled in Jesus, in delivering that required 'pound of flesh.'
The only reason, under this atonement theory, that God doesn't punish people is because Jesus was punished. And to me, that violates the definition of forgiveness, because God didn't give a need for satisfaction, God didn't "cease" to feel anything about sin. The only reason why he ceased is because the person's punishment was still meted out, only not to the person.
That's not forgiveness, that's a transaction. It becomes an 'if-then' statement, it becomes a system of rewards, and paints a rather poor picture of how God forgives. I'm not even sure you can say it's unconditional forgiveness, because quite a few conditions were set before forgiveness even took place.