We must throw off every encumbrance, every sin to which we cling. Heb. 12:1, N.E.B.
For many Christians the concept of sin centers on an angry God. "Jesus loves us, but God the Father...? Didn't Jesus have to die to get God to accept us? Sins are those things we do that make God mad--mad enough that someone has to pay the price, even though we stop doing them."
Though not painted with wild berry dye or adorned with carnivore teeth, these ideas belong to the heathen who serve their gods from fear. To obey God because we think He will remove His protective care from us if we don't is only one step removed from offering incense to a wooden idol. To say we obey God because we love Him, and still "know" that our obedience will incur His certain wrath, is to play a painful game of theological charade.
Realistically, if a branch is severed from the tree it will die, but not because the tree is angry at the branch. When our first parents allowed their doubts about God to sever their relationship with Him, God knew that they had no other means of survival. In order to give them (and us) the chance to understand this reality, God chose to allow that reality to be fulfilled on the cross. But not for a moment was it vengeance.
Why, then, has God used such words as wrath and vengeance in Holy Scripture? I think God meets us where we are. We do the same with our children, explaining things to them in a way they can understand, fully expecting them to grow into far more adequate explanations. To tell your college-age son that he needs to put oil in his car to keep it "happy" would be an insult to his intelligence. (Will his car not run, then, because it is "mad"?)
The problem with sin is not that it makes God angry but that it encumbers us! It keeps us from realizing God is our life Source. More than that, He is our quality of life! More than electricity in our brain, He is our encouragement to reason; more than strength to our limbs, He is our inspiration to climb to the heights.
God is interested in more than our survival; He is interested in the quality of our lives and, in direct relationship to this, the quality of our union with Him--our life source and our friend.