To answer your first point, you’re right. It is certainly impossible for the Catholic Church to deny some of the atrocities committed by some of her members and even in her name in the past. This is why recent popes have publicly apologized for the many atrocities committed by the Church throughout her 2000 year history.
It can also not be denied that various Orthodox Churches have likewise committed many atrocities against Catholics and even against their fellow Orthodox throughout the centuries.
On a personal level, I myself am a sinner, and it’s impossible for me to deny the sins I’ve committed in my past, which is why our Lord has blessed us with the Sacrament of Repentance (the “Second Baptism” as it’s called by many Eastern Catholics and Orthodox) and extended his loving mercy towards us.
Both the Catholic Church and the Orthodox Church(es) are made up of fallen human beings, who are liable to commit heinous acts even in the names of their particular Churches. That doesn’t invalidate the teachings of Jesus Christ as passed on through those Churches.