You have asked:
“What should I do if a parent of one of my church friends has anger management problems that are fuelling my friend’s depression and feelings of self-loathing? Is this a problem that I should bring to an elder or pastor of my congregation or is this a family issue I should stay out of?”
It sounds like both the parent and your friend need some help. You may be right that your friend has these feelings because of his angry parent, but that isn’t necessarily the case. Therefore, don’t assume that your friends problems are a direct result of his parents problems. Getting some help for your friend is crucial. While circumstances can contribute to depression there are plenty of occasions in the Bible and church history where one of God’s saints lives in desperate circumstances but nevertheless is happy and content. (Acts 16:25; Philippians 4:10-13).
What kind of help is available for your friend?
First of all, don’t underestimate the value of your friendship with him. He needs Christian friends to encourage him in the way of the Lord! (Acts 4:36) Be such a friend to him! Pray for him!
Second, encourage him to speak to his pastor and/or elder about his struggles also in regards to his home life. They may be able to get involved in the situation in his home in an effective pastoral way.
Third, get him a copy of Dr. Murray’s book on depression which is titled: “Christians Get Depressed Too.” This is a very practical resource that will help him in his situation.