St. FRED? Did he publish?
Okay, let me struggle with your first quote one second, and amazingly, I'll argue that it's not representative of what we think about Atonement in general. Yeah, I know: Color you surprised. It's from an article about Spirituality. A big thing for us is identifying with Christ. And that gets us in almost as much trouble as "Mother of God", I guess. Note that what you underlined was about how "we atone to Christ" It presupposes the Atonement wrought in Christ. But we seek to participate in the work of Atonement -- and at least in my case I know that's preposterous of me, but what can I say, I like going overboard -- So we pray for others sins, fast for others' sins. In some other conversation about the Catholic view of works, I compared us to a very little child watching his father or her mother, and "helping". And you know how much "help" that can be. Mom bakes the cake, but Sissie licked the mixing spoon so she "helped". Jesus dies horribly for the world as the climax to the humiliation of the Incarnation. We skip dessert. I'm kind of hoping that God thinks that's cute.
Maybe I'm overstating our view of the uselessness of it all. Certainly when I'm fasting (something I do too rarely) I think I have real discomfort and I trust that God will use that the way he uses prayer, in a mysterious way, utterly incomprehensible to me, to do what HE does.
So that's about what I facetiously call spearchool atonement. It is built on Christ's "all sufficient merit".
Now, after our last exchange and as I began to get the idea that we are talking past each other - or at least I'm missing everything coming in my direction, I actually looked at that article fairly closely, not just looking for "See THERE?" quotes.
And what I got was what I expected: The Atonement is a HUGE mystery. The whole "work of Christ", but especially the Death on the Cross, accomplishes what can not be accomplished by any mere creature, the reconciliation of Creation and Creator. So the blood shed during the Crucifixion -- and the mysterious water and blood from His pierced side -- is central, critical, at the core of the Atoning work.
There is a problem with the idea that God needs to be propitiated (That word, hilasmos, is interesting.), but there is also a problem with what the Justice of God is if there is not to be some dreadful consequence to the dreadful act of disobedience which Sin is. It's all very well for me to say "Mercy is the perfection of justice" but sometimes trying to think about it is as useful (to me at any rate) as thinking about the sound of one hand. My response is, "Wha'?"
Certainly the notion of Satisfaction is not totally discarded in our thinking. But it's not currently the front runner either. And I think the Satisfactory doctrine is the one closest to what you may mean by "blood atonement".
The sentence we have been sparring over leaves out my favorite (Jesus stomps the devil) but, I think, makes conscious reference to the other theories I have mentioned. It's an effort, I think, at a summation of the thinking about the atonement.
Okay, darn it, I have to go get ready to go out. I hope I have moved this forward a little. I'll very much look forward to hearing from you, but I won't get back until late tonight or sometime tomorrow.
2) I misread the doctrine of Atonement, and
3) the Atonement is a mystery to Catholics.
I suppose I can be forgiven for my confusion as to what Catholics truly believe about the Atonement, since Catholics don't seem to know and official websites are erroneous or unclear. One has to wonder how Catholics could develop traditions when so much is in error and confusing.
Since I don't seem to know what I'm talking about after providing multiple Catholic sources on the topic, then I would suggest you provide a reference to a short doctrinal statement as to what Catholics believe on the Atonement.