“I can’t offer up what doesn’t belong to me.”
Yes, you can. Even if you have no ownership over something you can still have use of it. Thus, you can offer up something that may not belong to you. All things belong to God, but the Jews were still able to offer up sacrifices.
“It is she who has suckled Him, nourished Him, supported Him, brought Him up, and then sacrificed Him for us.”
Mary can only take any credit for nursing Him, which ANY mother would have done for her child.
She did not raise Him single-handedly, there is no record that she supported Him, and she most certainly did not sacrifice Him for us. She did not offer Jesus as a sacrifice for our sins to appease God.
Catholics seem have this problem in understanding just who did the laying down of Jesus' life. Nobody gave us Jesus so that we could in turn offer Him to God for the propitiation of our sins. He is not being used by anybody to appease God.
Jesus offered up Himself, taking the punishment for our sins upon Himself to satisfy the justice of God.
Mary did nothing for Him that any other mother would not have done for their child. Scripture gives every indication that she didn't really understand Jesus and His ministry while He was still alive on this planet.
She can't take any more credit for what God did through her than anyone else can take for what God does through them. Nor does she deserve it.