The problem with analogies is that at some point, they almost always fail. While the illustration does not give sufficient account of the biblical portrait of man (the man would need to be dead at the bottom of the river) it does achieve the purpose of answering the specific question, “Which of those three men is the truest illustration of what God does to save us?”
“Long ago, when I was an undergraduate, I had an experience on one of the rivers in Oxford where students love to pole themselves around in flat-bottomed boats called punts. I do not know if undergraduates do it in the universities of this country, but we do it in Oxford. The experience was my falling into the river. I can still remember the surprise I had when I suddenly found myself upside down in the water and that there were strands of green weed around my head and the light was up at my feet. You do not forget that sort of thing quickly, and on the basis of that experience I construct for you the following illustration.
Imagine a man who has fallen into a river. He cannot swim. The weeds have caught his feet. He is threshing around, but he cannot get free and will not be above the surface for very long. His state is desperate. Three people come along on the bank. One looks at him and says, ‘Oh, he’s all right; if he struggles he’ll get out; they always do. It’s even good for his character that he should have to struggle like this. I’ll leave him.’
The second person looks at the poor struggling man and says, ‘I’d like to help you. I can see what you need. You need some tips about swimming. Let me tell you how to swim.’ He gives him a great of good advice, but he stops there.
Then there is the third man who comes along and sees the measure of the trouble. He jumps in, overcomes the man’s struggles, gets him free from the weeds that have caught him, brings him to shore, gives him artificial respiration, and puts him back on his feet. Which of those three men is the truest illustration of what God does to save us?
These three views have theological names. The first corresponds to what is called Pelagianism: its only message is self-help. A hard and unfeeling form of Christianity it is. The second corresponds to what is called Arminianism: God tells us how to be saved, but stops there. The third corresponds to Calvinism. And you can see how the illustration fits. God takes the initiative. Christ comes right down to where we are, enters into our trouble, and does all that has to be done. He breaks the bonds of sin that bind us, brings us to land (that is, to God), restores life, and makes us believers, all this by his sovereign grace which saves absolutely and wonderfully from first to last.”
“To All Who Will Come,” in Serving the People of God: The Collected Shorter Writings of J. I. Packer, Volume 2 (Paternoster Press), 200-01.