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I have a vivid memory from when I was about eight. As was his custom, and with his eyes and facial expression communicating utter contempt, my father told me off for some perceived minor misdemeanour which I didn't understand. I tried to voice an apology, but I was so scared, my mouth dried up and I couldn't get any words out. I always avoided making direct eye contact with him. My father then upped the ante and really went for me, I guess interpreting my silence as insolence. At that point my uncle Frank spoke up in my defence. "Tom, he was trying to apologise, but he couldn't get his words out." That was the one and only time I can remember anyone standing up for me and defending me in my childhood years. Uncle Frank became my hero. He was my advocate.
"My dear children, I write this to you so that you will not sin. But if anybody does sin, we have an advocate with the Father – Jesus Christ, the Righteous One. He is the atoning sacrifice for our sins [turning away God's wrath], and not only for ours but also for the sins of the whole world" (1 John 2:1-2). (What follows owes a lot to Dane Ortlund.)
Intercession has the idea of someone mediating between two parties and bringing them together. It goes on continuously. Advocacy has the idea of someone standing alongside one party as he approaches another. It happens whenever specifically needed. An advocate is a helper, defender, counsellor, comforter and companion; one who feels what we feel and speaks up for us on our behalf out of deep love and commitment to us. When does Christ do this? All the time! Even our best repenting of our sin is itself plagued with more sin needing more forgiveness. We have mixed motives and can't really feel the deepest godly sorrow.
Christ as our high priest goes before; continually intercedes; always acts and does so in the day-to-day aspects of our lives; Christ as our advocate comes after; in cases of greater transgression, pleads; sometimes acts and does so in times of big sins. Why? So we don't lose heart and give up in despair. He cannot bear to leave us to fend for ourselves. With every accusation the devil brings, he pleads our cause. He never says in a judgmental way "You should know better!" Rather he fights our corner affirming there is now no condemnation to those who are in Christ Jesus because there is no condemnation in God's heart towards those who have gratefully received his gift of salvation.
There is no reluctance on the Father's part that needs his Son's advocacy to work in our favour and on our behalf. The Trinity works as a perfect unity and all share exactly the same heart of meekness and accessibility, mercy and grace. They all want us to be fully aware and convinced that when we sin, mess up, give in to pride, believe the devil's lies, etc., they are all on our side, working together as one with us so we can gain the victory in the here-and-now, and make real progress in being made holy and more like Jesus.