"If anyone sins, we have an Advocate with the Father, Jesus Christ the righteous, and he himself is the atoning sacrifice for our sins, and not only for our sins but also for the whole world." (1 John 2:1-2)
Advocate is a bad word to use because it makes it seem as if the Father wants to kill or hurt us if Jesus doesn't convince Him not to, that Jesus must plead on our behalf to keep the Father's wrath at bay. The word would be better translated as "helper" or "comforter" as it is the same words used by Jesus for the Holy Spirit in John chapters 14-16. We have an advocate WITH the Father as in the Father is our helper too. They both help us. They both comfort us.
"Jesus himself is the atoning sacrifice for our sins." Atoning/propitiation could be translated as satisfying, satisfaction, content, contentment.
Of course God is unsatisfied to not have a relationship with us. Jesus's sacrifice opened to us the door of that relationship. God is satisfied when we enter that door because He wants to know us but these scriptures don't picture God aiming to please Himself. It is God aiming to please us so that if sin ever comes to our mind we can be completely secure in the fact that He has taken care of it for us. Sin was our problem that God fixed not God's problem because He has issues with anger.
"Jesus himself is the satisfying sacrifice for our sins." That means WE CAN be satisfied with nothing else but His sacrifice concerning our sins. His sacrifice satisfies us concerning "sin" to where we can need nothing else; not our performance, behavior, emotions; to make us confident that we know God without barriers, are fully reconciled to God, & fully cleansed of sin/failure.
John is saying Jesus's sacrifice IS enough to assure us beyond doubt that our sins are taken away & forgotten forever. His sacrifice IS enough to make us content, satisfied, & fulfilled in regards to knowing that our relationship with God is secure. And yes it satisfied God to do this for us.
How distant is this from the typical interpretations which say, "God the Father hates us (gets offended) so much when we sin but Jesus will keep Him off our backs if we tell Him what we've done wrong. Jesus stepped in & appeased God's wrath for us because God really wanted to kill us all." That is the message that words like atonement & advocate convey. That God was so against us He just had to keep Himself from going nuts on us by killing His Son.
Jesus revealed that the Spirit is our comforter. Here John reveals that Jesus is also our comforter with the Father because the Father is our comforter too. They comfort us by reminding us that Jesus's sacrifice for the world can completely satisfy us & make us content with God because our sins are no more. 1 John 4:10 says, "This is love, not that we loved God, but that he loved us, and sent his Son to give us contentment concerning our sins." That means no more worry or fear concerning sin EVER! It's true! It's true! I know it & I live it.